Question

Look at the proof showing sin^4 x = 3 - 4 cos 2x + cos 4x / 8. Which expression will complete the fourth step of the proof ?

Answer 1

The answer is the first one ⇒
`(1-2cos2x+(1+cos4x)/(2))/(4)`

Explanation:

∵ cos4x = 2cos²2x - 1

∴ cos²2x = (1 + cos4x)/2

∴
`sinx^(4)x=(1-2cos2x+(1+cos4x)/(2))/(4)` ⇒ ×2 up and down

`=(2-4cos2x+1+cos4x)/(8)`

`=(3-4cos2x+cos4x)/(8)`