Question

PLEASE HELP

Look at the proof showing sin^4x=3-4cos2x+cos4x/8. Which expression will complete the fourth step of the proof?
sin^4x=(sin^2x)^2
sin^4x=(1-cos2x/2)^2
sin^4x=1-2cos2x+cos^22x/4
sin^4x=?
A.) 1-2cos2x+(1+cos4x/2)/4
B.)1-2cos2x+1+cos4x/4
C.)1-2cos2x+(1+cos2x/2)/4
D.)1-2cos2x+1-cos2x/4

Answer 1

A
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Answer 2

Option 1 is correct.

Explanation:

Given the expression

`sin^4x=(1)/(8){(3-4cos2x+cos4x)}`

we have to complete the fourth step to prove the above result.

`sin^4x=(sin^2x)^2\\\\sin^4x=((1-cos2x)/(2))^2 \\\\sin^4x=(1-2cos2x+cos^22x)/(4)`

As,
`cos^2x=(1+cos2x)/(2)`

⇒
`cos^(2)2x=(1+cos4x)/(2)`

Hence, the next step becomes

`sin^4x=(1-2cos2x+(1+cos4x)/(2))/(4)`

Hence, option 1 is correct.