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

Answer:

Option 1 is correct.

Step-by-step explanation:

Given the expression

$sin^4x=\frac{1}{8}{(3-4cos2x+cos4x)}$

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

$sin^4x=(sin^2x)^2\\\\sin^4x=(\frac{1-cos2x}{2})^2 \\\\sin^4x=\frac{1-2cos2x+cos^22x}{4}$

As, $cos^2x=\frac{1+cos2x}{2}$

⇒  $cos^{2}2x=\frac{1+cos4x}{2}$

Hence, the next step becomes

$sin^4x=\frac{1-2cos2x+\frac{1+cos4x}{2}}{4}$

Hence, option 1 is correct.