(sec 12A - 1)/(sec 6A -1) = tan 12A / tan 3A
Answers
To prove the given trigonometric identity:
(sec 12A - 1)/(sec 6A -1) = tan 12A / tan 3A
We will proceed by transforming the left side of this identity and attempt to simplify it to the form of the right side. First, let's use the trigonometric identities.
Secant and tan identities are key to simplifying this expression. It's important to note that:
sec(x) = 1/cos(x)
tan(x) = sin(x)/cos(x)
Let's rewrite the left side of the equation using these identities:
((1/cos(12A)) - 1) / ((1/cos(6A)) -1)
Now bring each term over a common denominator:
((1 - cos(12A))/cos(12A)) / ((1 - cos(6A))/cos(6A))
By simplifying the complex fraction, we get:
(cos(6A) - cos(12A)) / (cos(12A) - 1)
Next, we can use the following identity to transform the numerator: sin(A+B) = sin A cos B + cos A sin B.
Applying a form of this identity to cos(6A - 12A), we get that the numerator is equivalent to -sin(6A)sin(12A).
Similarly, we can express tan 12A as sin(12A)/cos(12A) and tan 3A as sin(3A)/cos(3A).
Substituting these into our original equation, we obtain:
(-sin(6A) * sin(12A)) / sin(12A) * cos(3A) = tan 12A / tan 3A
After canceling out sin(12A) from the numerator and denominator, we are left with:
-sin(6A) / cos(3A) = tan 12A / tan 3A
Given that sin(6A) = 2sin(3A)cos(3A), the left-hand side simplifies to 2 * tan 3A, and since tan 3A is equivalent to sin(3A)/cos(3A), the expression simplifies to tan 12A / tan 3A, proving the identity.
Related Questions
The area of the triangle shown is represented by A= square root of s(s-10)(s-7)(s-5), where s is equal to half the perimeter. What is the height of the triangle? Round your answer to the nearest tenth.
Answers
S is half the perimeter, so .5*(7+5+10)=11
Plug in 11 and you get A=sqrt(264)
A also is half base times height
sqrt(264)=.5*10*h
h=sqrt(264)/5
h=3.25
Rectangle ABCD is similar to rectangle QRST. The width of ABCD is 5 inches and the length is 8 inches. If the length of QRST is 12 inches, what is the width of QRST?
Answers
Form your proportion. Let x be the width of QRST.
Length of ABCD Length of QRST
----------------------- = -------------------------
Width of ABCD Width of QRST
8/5 = 12/x
Solve for x by cross-multiplying.
(8)(x) = (12)(5)
8x = 60
x = 7.5
Answer:
7.5
Step-by-step explanation:
There are 52 blades of grass in 2 in2 of lawn. There are 580 blades of grass in 8 in2 of the same lawn. Which equation models the y blades of grass found in x in2 of lawn?
Answers
The equation that models the relationship between the number of blades of grass (y) and the area of lawn (x) is y=88x−124. This equation represents the rate of 88 blades per square inch with an initial count of 52 blades.
To find the equation that models the relationship between the number of blades of grass (y) and the area of lawn (x), we can use the given information to form a linear equation.
Step 1: Determine the rate of change. Subtract the initial number of blades from the final number and divide by the change in area: (580 - 52) / (8 - 2) = 528 / 6 = 88 blades per square inch.
Step 2: Write the equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
Step 3: Plug in the slope (m = 88) and one point (x = 2, y = 52) to find the y-intercept:
52 = 88(2) + b
52 = 176 + b
b = -124
Step 4: Write the equation:
y = 88x - 124
The scatterplot below shows the number of hours that some high school students spend on working and on video games.
Which statement about the scatterplot is true?
In general, the number of hours spent working does not affect the number of hours spent on video games.
In general, the amount of weekly time spent working is equal to the amount of weekly time spent on video games.
As the amount of time spent working increases, the amount of time spent on video games increases.
As the number of hours spent working increases, the amount of time spent on video games decreases.
Answers
Going from left to right, we see that the points are moving down. This means that the hours working are going up and the video game hours are going down.
Answer:
D
Step-by-step explanation:
As the number of hours spent working increases, the amount of time spent on video games decreases.
Fiona earns $15 for each lawn she mows. Which inequality can be used to find out how many lawns she must mow to earn at least $135?
Answers
Final answer:
Fiona needs to mow at least 9 lawns to earn at least $135, represented by the inequality 15L ≥ 135, where L is the number of lawns mowed.
Explanation:
To determine how many lawns Fiona must mow to earn at least $135, we can set up an inequality. Fiona earns $15 for each lawn she mows, therefore if we let L represent the number of lawns mowed, then Fiona's earnings can be represented by 15L. She needs to earn at least $135, so we can write the inequality as 15L ≥ 135. To find L, we divide both sides of the inequality by 15, which gives us L ≥ 9. Therefore, Fiona must mow at least 9 lawns to earn at least $135.
A savings account was opened with an initial deposit and never touched again. An account that does not meet the minimum balance requirement is charged a service fee.
Assuming the account was open with an initial deposit below the minimum amount, the current account balance, B, is equal to the product of the initial deposit, I, and the quantity of the difference of 1 and the monthly service fee, f, raised to the power of n, the number of months since the account was open.
If an initial deposit of $2,713.00 is made to the account with a monthly service fee of 5%, what will be the value of B after 13 months? Round to the nearest cent.
Answers
To find the current balance B after 13 months with an initial deposit of $2,713.00 and a 5% monthly service fee, you multiply the initial deposit by 0.95 to the power of 13, resulting in a balance of approximately $1,392.64.
Explanation:The student's question involves using a given mathematical formula to find the current balance of a savings account affected by a monthly service fee. The formula provided states that the current balance B is equal to the initial deposit I times the quantity (1 - monthly service fee f) raised to the power of the number of months n. To calculate the current balance after 13 months, given an initial deposit of $2,713.00 and a monthly service fee of 5%, you'd perform the following calculation:
Convert the percentage fee to a decimal: 5% = 0.05.Subtract the service fee from 1: 1 - 0.05 = 0.95.Raise the difference to the power of the number of months: 0.9513.Multiply the result by the initial deposit: $2,713.00 × 0.9513.Using a calculator, this gives:
B = $2,713.00 × (0.9513) ≈ $2,713.00 × 0.5133421 ≈ $1,392.64
Rounded to the nearest cent, the value of B after 13 months is $1,392.64.
The driving distance from the Sports Arena to Christinas house is 10 9/10 miles the distance from the Sports Arena to Luke’s house is 2 7/10 Miles how much greater is the driving distance between the sports arena in Kristen’s house then between the sports arena in Luke’s house
Answers
(10-2)+(9-7)
answer is 8 2/10 miles greater
Is my answer correct?
Will give brainliest!!
Answers
What is the relationship between radius and diameter of a circle
Answers
The diameter of a circle is all the way in the center.
( there is a picture to give you a visual understanding ) :)
If you have any questions be free to ask!!!!!! :)
2/3 - 1/6 finding the common denominator show me how to do it
Answers
Write an exponential growth function to model each situation. Please answer questions 1 2 3 and 4
Answers
8 years: 549,613.43
2.y= 4200(1.03)^x
7 years: 5165
3.y= 350000(0.97)^x
6 months: 291540.20
4.y=1200(0.98)^x
5 years: 1084
Which sentence best describes the function shown?
A) The function is odd.
B) The function is even.
C) The function is symmetric about the x-axis.
D) The function is symmetric about the origin.
Answers
Answer:
B) The function is even.
Step-by-step explanation:
The function shown in the graph is ƒ(x) = |x|. This function is symmetric about the y-axis and is therefore, even.
In simple words: If you fold the picture in half then the lines should be on top of each other and become one. If this happens, then this is an even function.
round each amount to the nearest hundred to find an estimate of: 3891÷289
Answers
13.5,
OR
13.46,
hope this helped
the full answer is 13.4636678201
Here’s another for you people - 5/6k = 1/6
Answers
(-5 k)/6 = 1/6
Multiply both sides of (-5 k)/6 = 1/6 by -6/5:
(-6 (-5) k)/(5×6) = ((-6)/5)/6
(-6)/5×(-5)/6 = (-6 (-5))/(5×6):
(-6 (-5))/(5×6) k = ((-6)/5)/6
((-6)/5)/6 = (-6)/(5×6):
(-6 (-5) k)/(5×6) = (-6)/(5×6)
(-6)/6 = (6 (-1))/6 = -1:
(-5-1 k)/5 = (-6)/(5×6)
(-5)/5 = (5 (-1))/5 = -1:
--1 k = (-6)/(5×6)
(-1)^2 = 1:
k = (-6)/(5×6)
(-6)/6 = (6 (-1))/6 = -1:
Answer: k = (-1)/5
1.3-2.1g when g is 1.9. Can you please help? I keep getting 2.69 but the paper shows the answer to be 5.29
Answers
Draw two different figures that each have a perimeter of 20 units
Answers
What is the differencence betwenn the volume
Answers
12*2*7 3/4=186cubic inches
big box height =12/80%=15
big box volume=15*2*7 3/4=232.5cubic inches
difference=232.5-186=46.5 cubic inches
You are playing a game and it is your turn to spin the spinner shown. There are four possible results: blue, green, yellow, or purple. What is the probability that you land on purple?
Answers
You have a 25% chance on landing on any of the colors
You Look at all of the possible ways you can land on which is purple, Blue, Green, and Yellow there are four colors in the spinner if you divide the number of colors (4) and divide it by 100 you will get 25 and that is your answer
Which ordered pair is a solution to the system of equations?
Answers
Then solve for y, using the x value that you have solved for.
Or after substituting both equations. To make one large equation, plug in each point for x and y values.
Then see if the left side equals the right side of the equation.
Which word has line symmetry, DAD, ODE, or HOME
Answers
_________________
hope my answer helped, have a good day
At a certain time of day, a 30-foot building casts a 10 foot shadow. How tall is a person who casts a 2 foot shadow?
A. 4 feet
B. 5 feet
C. 6 feet
D. 7 feet
Answers
3 * 2 = 6
A person who is 6 feet tall casts a 2 foot shadow.
The correct answer is C. 6 feet.
hope this helps!! have a good day!! :)
Horace buys 2/4 pounds of blueberries for a pie he needs 48 ounces for the pie how many more pounds of blueberries does he need to buy
Answers
Horace need to buys 2.5 pounds of blueberries
Horace buys 2/4 pounds of blueberries48 ounce of blueberries needed for a pieTo determine how many pounds of blueberries that Horace need to buy, we have to convert ounces because this mathematical question is related to unit conversion.Further Explanation1 pounds = 16 ounces, therefore,
3 pounds = 48 ounces (we multiply 16 and 3 = 48)
To find how many pounds he need to by = 3 ounces – [tex]\frac{2}{4}[/tex]
= 3 – [tex]\frac{2}{4}[/tex]
= [tex]\frac{3}{1}[/tex] – [tex]\frac{2}{4}[/tex] (4 is the smallest number can divide both denominator) therefore, we have
= (4 x 3) – (1 x 2) / 4
= 12 - 2 / 4
= [tex]\frac{10}{4}[/tex]
= 2.5
Thus, Horace buys 2.5 pounds of blueberries.
LEARN MORE:
The canadian side of niagara falls has a flow rate of 600000 gallons per second how many gallons of water flow over the falls in one minute brainly.com/question/3524504Charlotte is traveling 15 meters per second. Which expression could be used to convert this speed to kilometers per hour brainly.com/question/11053063KEYWORDS:
Horace2/4 poundsblueberriespie48 ounces. Greg has a school debt of $9 875. He wants to make biweekly payments and pay off the loan in 4 years. If the interest rate is 6.3% compounded biweekly, how much are his payments?
Answers
A party is thrown where 25 tables are used. Each table either sits 4people or 6 people. A total of 116 people can be sat at the tables.
1- if f represent the number of four person tables and s represents the number of six person tables, write a system of equations that models this equation.
2- how many six person tables are there?
Answers
s= x = 4-person tables
a= y = 6-person tables
x + y = 25
~ You use 25 tables so no matter how many of each kind are there, you end up with 25 tables so it should add up to 25.
4x + 6y = 116
~ You know that there will always be a total of 116 people at the tables. And in this case 4 and 6 are the number of people that can be seated at these tables, so in terms of people, you would say 4x and 6y.
To find out the amount of six people tables, solve for y and that's your answer.
You could do this a variety of ways.
One way is the substitution, for that you would rearrange the first equation for y, then plug in that value for y in the second equation and then solve for y. That value you get is your answer.
There are two prominent, nationally circulated newspapers, The Wall Street Journal and USA Today. Among all libraries across the country, 45% subscribe to The Wall Street Journal and 40% subscribe to USA Today, while only 25% subscribe to both The Wall Street Journal and USA Today. If a library is selected at random, what is the probability that it subscribes to The Wall Street Journal but not USA Today?
Answers
P(A∩B^c), or the intersection of A and Not B happening.
P(A∩B^c)=P(A∪B)-P(B) = [P(A)+P(B)-P(A and B)]-P(B)
=(0.45+0.40-0.25)-0.40 = 0.2.
Answer:
20% = 0.2
Step-by-step explanation:
Let A = Wall Street Journal = 45%
Let B = USA Today = 40%
Let C = Both = 25%
C = A∩B = 25%
The focus is to determine that a random library subscribes to A only
The probability of subscribing to A = 45%
However, there are subscribers to A that are also subsribed to B
This group is C = 25%
To find the probability of subscribing to A only;
Probability of A only = P{A} - P{A∩B} = P{A} - P{C}
P{A} only = 45% - 25% = 20%
P{A} only = 0.2
Zacarias and Paz together have $756.80. If Zacarias has $489.50, how much does Paz have? Write and solve an addition equation to find how much money belongs to Paz
Answers
You have to subtract and do 756.80-489.50 to find out how much money Paz has
It equals 267.3
Paz has $267.3
0.746, 0.745, 0.75 in order from largest to smallest. Please
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4) A sales associate in a department store earns a commission on each suit and each pair of shoes sold. One week, she earned $47 in commission for selling 3 suits and a pair of shoes. The next week, she earned $107 in commission for selling 7 suits and 2 pairs of shoes.
a) Write a system of equations to represent the situation. Explain what your x and y will represent.
b) Solve the system of equations.
c) How much commission does she earn for selling each suit and each pair of shoes?
Answers
The sales associate earns a commission of $13 for each suit sold and $8 for each pair of shoes sold, found by solving the system of equations representing her commission earnings for two different weeks.
To represent the sales associate's commission earnings, we will use two variables: let x be the commission for each suit sold, and y be the commission for each pair of shoes sold.
(a) System of Equations:
The first week's commission can be represented by the equation 3x + y = 47. The second week's commission can be written as 7x + 2y = 107.
(b) Solving the System:
Multiply the first equation by 2 to get 6x + 2y = 94.Subtract the first modified equation from the second week's equation: (7x + 2y) - (6x + 2y) = 107 - 94.This simplifies to x = 13, meaning the commission for each suit is $13.Substitute x = 13 into the first equation: 3(13) + y = 47.Solve for y: 39 + y = 47, so y = 8.(c) The commission for each pair of shoes is $8.
How many rectangular faces does a hexagonal pyramid have ?
Answers
A cube-shaped item needs to be painted. The item’s edge length is 2 centimeters. What is the total surface area that will be painted? 16 cm² 24 cm² 32 cm² 48 cm²
Answers
By definition, the surface area of a cube is given by:
[tex]A = 6L ^ 2 [/tex]
Where,
L: length of the sides of the cube.
Substituting values we have:
[tex]A = 6 (2) ^ 2 A = 6 (4) A = 24 cm ^ 2[/tex]
Answer:
The total surface area that will be painted is:
24 cm²
Answer: A) 24
Hope This Helps ^_^