Answers
Answer: see proof below
Step-by-step explanation:
Use the following Half-Angle Identities:
sin² A = (1 - cos 2A)/2
cos² A = (1 + cos 2A)/2
Proof LHS → RHS:
LHS: sin⁴ A
Expand: sin² A · sin² A
[tex]\text{Half-Angle:}\qquad \qquad \bigg(\dfrac{1-\cos (2A)}{2}\bigg)\bigg(\dfrac{1-\cos (2A)}{2}\bigg)[/tex]
[tex]\text{Distribute:}\qquad \qquad \dfrac{1-2\cos (2A)+\cos^2 (2A)}{4}[/tex]
[tex]\text{Half-Angle:}\qquad \qquad \dfrac{1-2\cos (2A)+\frac{1+\cos (2\cdot 2A)}{2}}{4}[/tex]
[tex]\text{Simplify:}\qquad \qquad \dfrac{\frac{2}{2}[1-2\cos (2A)]+\frac{1+\cos (4A)}{2}}{4}[/tex]
[tex]=\dfrac{2-4\cos (2A) + 1 + \cos (4A)}{8}[/tex]
[tex]=\dfrac{1}{8}\bigg(3-4\cos (2A)+\cos (4A)\bigg)[/tex]
LHS = RHS [tex]\checkmark[/tex]
Let's start from LHS...
LHS = sin^4A = sin^2A * sin^2A
We can apply a few formulas here;
cos 2A = 1 - 2sin^2A
sin^2A = (1 - cos2A) / 2
cos2A = 2cos^2A - 1
cos^2A = (1 + cos2A) / 2
According to the second formula, sin^2A * sin^2A = (1 - cos2A) / 2 * (1 - cos2A) / 2.
(1 - cos2A) / 2 * (1 - cos2A) / 2 = 1/4(1 - cos2A)^2
We can simplify "(1 - cos2A)^2." Remember that (a - b)^2 = a^2 - 2ab + b^2. Similarly (1 - cos2A)^2 = (1 - 2cos 2A + cos^2 2A);
1/4(1 - cos2A)^2 = 1/4(1 - 2cos 2A + cos^2 2A)
According to the fourth formula, cos^2 2A = (1 + cos4A) / 2;
1/4(1 - 2cos 2A + cos^2 2A) = 1/4(1 - 2cos 2A + (1 + cos4A) / 2)
= (taking LCM) 1/4( (2 - 4cos 2A + 1 + cos4A)/2 )
= (simplified) 1/8(3 - 4cos 2A + cos 4A)
Related Questions
What 3 numbers can be multiplied together to get 180?
Answers
2×6×15=180
Step-by-step explanation:
2×6=12
12×15=180
Answer:
3×6×10=180
Step-by-step explanation:
.............. there can be more than one right answer for this
Find the missing number.
3 + 8 + 4 + 9 = (12 + ____) + 9
Answers
Answer:
3!
Step-by-step explanation:
Add 3+8+4+9, you get 24. 12+9=21. 24-21 is 3! So answer is 3!
10 pls 10 I dnt no wat to do
Answers
Solve x-(-9) = -14.
0-5
0 23
0-23
O 5
Answers
Step-by-step explanation:
x - (-9) = -14
x = -14 +(-9)
x = - 23
if you wanna check,
-23 - (-9) = -14
-14 = -14
Which vehicle has the better gas mileage? Explain your reasoning.
Answers
Answer:
Tesla because it has no gas
At a music store, 8 CDs cost 32$. How much will 15 CDs cost at this store?
Answers
Answer:
$60
Step-by-step explanation:
First we have to find the default cost for a single CD.
8 ÷ 32
Divide.
8 ÷ 32 = 4
Now that we have the default cost, we have to find the price for 15 CDs.
4 x 15
Multiply.
4 x 15 = 60
If three boxes of pasta cost $5.79, find the cost of 22 boxes.
Answers
Answer:
Step-by-step explanation:
3 boxes of pasta --> $5.79
1 box of pasta --> $5.79/3=$1.93
22 boxes of pasta --> $1.93 x 22 =$42.26
How I got the answer divide 5.79 by 3 three multiply the answer by 22 then you get the answer
What value of x satisfies the equation below?
x +x=12
3 6
A. x=12
B. x=6
C. x=24
D. x=72
Answers
Write a verbal statement that represents the expression 4+k
Answers
Answer:
it would be 4k
Step-by-step explanation:
just add 4 and the k which gives you 4k
......
Any help on this maths question will be truly appreciated
Answers
Step-by-step explanation:
Hey there!
1. 》 (√5)^2*(√3)^2
Cancel sqrt and square.
[tex]5 \times 3[/tex]
= 15
2.
[tex] = { (\sqrt[ 3]{9} )}^{3} \times ( { \sqrt{30}) }^{2} [/tex]
Cancel sqrt and square and also cubeoot and cube.
[tex]9 \times 30[/tex]
= 270
Hope it helps....
What will the 15th term in the sequence be? 2.2, 4.4, 6.6, 8.8,
Answers
Answer:
30.30
Step-by-step explanation:
Just count up by 2 each time.
What is an equivalent ratio to 9/15?
Answers
Answer:
the answer is 3/5
Step-by-step explanation:
Answer:
3/5
Step-by-step explanation:
I’m just different
Which property explains why these two expressions are equal?
a(b + c) = a(c + b)
Answers
Answer:
The Associative Property.
Answer:
They are equal because no matter how you flip an addition equation, the result will always be the same. aka the associative property.
Step-by-step explanation:
Because variable a never moved, but b and c did, the answer remains the same.
example: x + y = y + x
6. Write an equation of a line that passes through the points (4,5) and (8,3).
Answers
Answer:
The answer to your question is -2/4
Step-by-step explanation:
y2-y1
x2-x1
the sum of 1/11 and 5/11
Answers
Answer:
6/11
Step-by-step explanation:
1/11+5/11
Answer:
the sum of 1/11 and 5/11 is 6/11
Step-by-step explanation:
the sum would mean addition so
1/11 + 5/11
when adding fractions you don't add the denominator
so then you'd only add 1 + 5 which gets you 6
so 6/11
Sofia wants to rent an apartment. She visits Apartment A which charges $100 for a one-time deposit and $400 per month for rent. She also visits Apartment B which charges $500 for a deposit, but only charges $350 per month in rent. Write and solve an inequality that shows how many months it would take for the total paid to be less for Apartment B.
Answers
Credit To: "lublana" On Brainly For This Answer
Answer:
Given that one time charge of appartment "a" = $100
Given that monthly rent of appartment "a" = $400
say the number of months = x
then total cost of the rent for apartment "a" = 100+400x
Given that one time charge of appartment "b" = $500
Given that monthly rent of appartment "b" = $350
then total cost of the rent for apartment "b" = 500+350x
Now we have to make an inequality so that number of months it would take for the total paid to be less for apartment b.
that means 100+400x is less than 500+350x
Hence required inequality is 100+400x<500+350x.
Now we have to solve this inequality.
400x-350x<500-100
50x<400
divide both side by 50
x<8
hence final answer is number of months should be less than 8.
How can ΔWXY be mapped to ΔMNQ?
Triangles W X Y and M N Q are shown. The lengths of sides M N and W X are 18 centimeters. The lengths of sides Y W and M Q are 30 centimeters. Angles Y W X and N M Q are congruent. Triangle W X Y is slightly up and to the right of triangle M N Q. Angle Y W X is the bottom angle and angle N M Q is the left angle.
Translate vertex W to vertex M, then reflect across the line containing _______________.
Answers
Answer:
A. WX
Step-by-step explanation:
May I have brainliest please? :)
Triangle WXY can be mapped to triangle MNQ by:
Translating vertex W to vertex M.Then, reflect ΔWXY across the line containing line segment WX.What is transformation?Transformation involves changing the size and the position of a shape
From the figure (see attachment), we have the following highlights
Both triangles are not on the same height (i.e. translation is required)Both triangles are not on the same orientation (i.e. one of the triangles need to be reflected)Hence, Triangle WXY can be mapped to triangle MNQ by translating vertex W to vertex M, and then, reflecting ΔWXY across the line containing line segment WX.
Read more about transformation at:
https://brainly.com/question/4057530
Complete the long division problem on your own sheet of paper. Then, fill in the digits.
47 dived by 9598 do the whole problem
Answers
Answer:
204 Remainder 10 / 204 10/47
Step-by-step explanation:
Answer:
0 2 0 4
4 7 9 5 9 8
− 0
9 5
− 9 4
1 9
− 0
1 9 8
− 1 8 8
1 0
Step-by-step explanation:
the answer is 10
i need help;-; Like 25 points or something
Answers
Answer:
28.26
Step-by-step explanation:
area of a circle formula:
[tex]\pi \times r^{2} [/tex]
since we substitute pi for 3.14 it would be 3.14×(3)^2
3^2=9
9×3.14=28.26
Answer:
28.26
Step-by-step explanation:
hope this helps
Solve for r:
3x + 2 = 11
11
O A
B. 3
Oc.
3
OD.
13
3
O E 6
Answers
Answer:
B
Step-by-step explanation:
3x + 2 - 2 = 11 -2
3x = 9
3x divided by 3 = 9 divided by 3
x=3
Determine if segments JK and LM are parallel, perpendicular, or neither.
J(-10, -7) K(-4, 1) L(-1, 1) M(-6, -2)
Answers
Answer:
perpendicular
Step-by-step explanation:
the lines meet together
During a musical, an orchestra is playing. As the music plays, the volume changes at the beginning of the piece can be modeled by the equation s = 10│x - 4│+ 50 where s represents the sound level in decibels and x represents the number of measures of music played. Explain in words each step to find the following question:
At what number(s) measures played would the sound level be at 80 decibels?
Answers
Answer:
what
Step-by-step explanation:
...
Next, we subtract 50 from both sides of the equation.
Next, we divide both sides of the equation by 10
Next, to eliminate the absolute value bars, we will add a ± sign in front of our s value, 3.
Finally, we add 4 to both sides of our equation giving us 4 ± 3 = x
Separating this into two equations, we get 4 - 3 = x and 4 + 3 = x
Therefore, x, the number of measures of music played, must be either 1 or 7.
Can you find the mistake?
Answers
Answer:
14b +64
Step-by-step explanation:
as listed above
-4 5/1 as a simplified fraction?
Answers
What is the answer to 5x + 2 = 3x
Answers
Answer:
x = -1Explanation:
5x + 2 = 3x
5x - 3x = -2
2x = -2
x = [tex]\dfrac{-2}{2}[/tex]
x = -1
Hope this helps! ☺
Answer:
-1
Step-by-step explanation:
5x+2=3x
2=-2x
x=-1
Convert 250 pesos to U. S. dollars. The exchange rate is 9.99 pesos per U. S. dollar.
options
a. $30.02
b. $240.01
c. $259.99
d. $25.03
e. $2497.50
HELP NEEDED RIGHT AWAY PLS DUE NOW!!!!
Answers
Answer:
D
Step-by-step explanation:
250/9.99=25.0250... Round it to 25.03
The required converted value is $25.03, which is 250 pesos to U. S. dollars.
As we all know, unit conversion is the process of multiplying a provided quantity by a conversion factor that combines the two interconnected units.
To convert 250 pesos to U.S. dollars, we divide the amount of pesos by the exchange rate.
Here, the exchange rate is given as 9.99 pesos per U.S. dollar.
It is the process of assigning a quantity from one unit of measurement to another.
250 pesos / 9.99 pesos per U.S. dollar = 25.025 U.S. dollars
Rounding this to two decimal places, the conversion is approximately $25.03.
Therefore, the correct option is (d) $25.03.
Learn more about the conversions here:
brainly.com/question/3810064
#SPJ6
What is the difference between Glasgow and Copenhagen. (Glasgow= -7.8 Copenhagen=-3.8)
Answers
Answer:
Step-by-step explanation:
The difference of the two values is 4 as calculated by subtraction.
An arithmetic operation called subtraction is the process of deleting or removing items from a collection. The negative symbol (-) denotes subtraction.
Subtraction can mean eliminating or lowering physical and abstract quantities utilizing a variety of things, such as fractions, matrices, vectors, irrational numbers, decimals, functions, and however negative integers. it is typically linked with natural numbers in mathematics.There are several significant patterns in subtraction. It is anticommutative, which means that altering the sequence alters the answer's sign. Additionally, it is not associative, which means that when subtracting more than two numbers, the method used matters. 0 is the additive identity, hence subtracting it has no effect on a number. In relation to related operations like addition and multiplication, subtraction also abides by predictable principles.The given values for Glasgow and Copenhagen are given as -7.8 and -3.8 .
Therefore difference = -3.8 - (-7.8) = -3.8 +7.8 = 4
To learn more about subtraction visit:
https://brainly.com/question/2346316
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I need help pleasseseeee
Answers
Answer:
D, 110$
Step-by-step explanation:
According to the systematic function, given that the bill as a function is equal to one tenth the quantity of x for kilowatt hours less than or equal to 200, and three twentieths of 200 less than the quantity of x plus 20 for kilowatt hours greater than 200. The answer is 110$ because the question gives us a measure of kilowatts greater than 200 so the second equation is used in the system. Therefore .15(800-200) + 20 = b(800), (.15)600 +20 = 90 + 20 = 110
A cedar board is 2 inches long and 8 feet long. You will need to cut down the length of the board into 1 1/3 inches long. How many pieces can u cut from an 8 inch long board
Answers
Answer:
You will be able to cut at least 6 pieces
Step-by-step explanation:
An object with increasing acceleration is also increasing in which other property?
mass
velocity
temperature
volume
Answers
Answer:
The answer is Velocity
Step-by-step explanation:
I just took the test and it was the right answer.