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Question: If \(\cos x + \cos^{2}x = 1,\) then the value of \(\sin^{2}x + \sin^{4}x\) is...

If cos⁡x+cos⁡2x=1,\cos x + \cos^{2}x = 1, then the value of sin⁡2x+sin⁡4x\sin^{2}x + \sin^{4}x is

A

1

B

– 1

C

0

D

2

Answer

1

Explanation

Solution

cos⁡x+cos⁡2x=1⇒cos⁡x=sin⁡2x\cos x + \cos^{2}x = 1 \Rightarrow \cos x = \sin^{2}x

∴sin⁡2x+sin⁡4x=cos⁡x+cos⁡2x=1\therefore\sin^{2}x + \sin^{4}x = \cos x + \cos^{2}x = 1.