Answer: see proof below
<u>Step-by-step explanation:</u>
Use the following Half-Angle Identities:
sin² A = (1 - cos 2A)/2
cos² A = (1 + cos 2A)/2
<u>Proof LHS → RHS:</u>
LHS: sin⁴ A
Expand: sin² A · sin² A
![\text{Half-Angle:}\qquad \qquad \bigg(\dfrac{1-\cos (2A)}{2}\bigg)\bigg(\dfrac{1-\cos (2A)}{2}\bigg)](https://tex.z-dn.net/?f=%5Ctext%7BHalf-Angle%3A%7D%5Cqquad%20%5Cqquad%20%5Cbigg%28%5Cdfrac%7B1-%5Ccos%20%282A%29%7D%7B2%7D%5Cbigg%29%5Cbigg%28%5Cdfrac%7B1-%5Ccos%20%282A%29%7D%7B2%7D%5Cbigg%29)
![\text{Distribute:}\qquad \qquad \dfrac{1-2\cos (2A)+\cos^2 (2A)}{4}](https://tex.z-dn.net/?f=%5Ctext%7BDistribute%3A%7D%5Cqquad%20%5Cqquad%20%5Cdfrac%7B1-2%5Ccos%20%282A%29%2B%5Ccos%5E2%20%282A%29%7D%7B4%7D)
![\text{Half-Angle:}\qquad \qquad \dfrac{1-2\cos (2A)+\frac{1+\cos (2\cdot 2A)}{2}}{4}](https://tex.z-dn.net/?f=%5Ctext%7BHalf-Angle%3A%7D%5Cqquad%20%5Cqquad%20%5Cdfrac%7B1-2%5Ccos%20%282A%29%2B%5Cfrac%7B1%2B%5Ccos%20%282%5Ccdot%202A%29%7D%7B2%7D%7D%7B4%7D)
![\text{Simplify:}\qquad \qquad \dfrac{\frac{2}{2}[1-2\cos (2A)]+\frac{1+\cos (4A)}{2}}{4}](https://tex.z-dn.net/?f=%5Ctext%7BSimplify%3A%7D%5Cqquad%20%5Cqquad%20%5Cdfrac%7B%5Cfrac%7B2%7D%7B2%7D%5B1-2%5Ccos%20%282A%29%5D%2B%5Cfrac%7B1%2B%5Ccos%20%284A%29%7D%7B2%7D%7D%7B4%7D)
![=\dfrac{2-4\cos (2A) + 1 + \cos (4A)}{8}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B2-4%5Ccos%20%282A%29%20%2B%201%20%2B%20%5Ccos%20%284A%29%7D%7B8%7D)
![=\dfrac{1}{8}\bigg(3-4\cos (2A)+\cos (4A)\bigg)](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B1%7D%7B8%7D%5Cbigg%283-4%5Ccos%20%282A%29%2B%5Ccos%20%284A%29%5Cbigg%29)
LHS = RHS ![\checkmark](https://tex.z-dn.net/?f=%5Ccheckmark)
Answer:
it ia 44w and 53l and it will help with it
Step-by-step explanation:
Answer:
2x = 26, x = 13
Step-by-step explanation:
Write and solve an equation twice a number is 26
x = unknown number
Equation: 2x = 26
Solve:
2x = 26
/2 /2 <== divide both sides by 2
x = 13
Check your answer:
2x = 26
2(13) = 26
26 = 26
This stament is correct
Hope this helps!
Answer:
5
Step-by-step explanation:
I'm assuming you want to find the maximum value of y
recall that for any cosine function y = A cos ( g(x) ), where g(x) is any arbitrary function, that A represents the amplitude of the cosine function.
By definition, the amplitude is the maximum the value which the cosine term can take.
hence for your expression:
y= -1 + 6 cos ( 2π/7(x-5) )
max value of y = -1 + (max value of cosine function)
max value of y = -1 + (amplitude of cosine function)
max value of y = -1 + 6 = 5
I think is true
Please let me know if it right