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If sinx+sin2x+sin3x=1 then cos6x–4cos4x+8cos2x=

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a

1

b

2

c

3

d

4

answer is D.

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Detailed Solution

sinx(1+sin2x)=cos2x Squaring on both sidessin2x(2−cos2x)2=cos4x ⇒(1−cos2x)(4+cos4x−4cos2x)=cos4x ⇒4=cos6x−cos4x+8cos2x

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