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Question

If sinx+sin2x=1, then
cos12x+3cos10x+3cos8x+cos6x+2cos4x+cos2x2=

A
0
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B
1
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C
sin2x
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D
cos2x
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Solution

The correct option is C sin2x
sinx+sin2x=1sinx=cos2xcos12x+3cos10x+3cos8x+cos6x+2cos4x+cos2x2
=sin6x+3sin5x+3sin4x+sin3x+sin2x+sinx2
=[sin6x+sin3x+3sin5x+3sin4x]+[sin2x+sinx]2+sin2x
=[(sin2x)3+(sinx)3+3(sin2x)(sinx)(sin2x+sinx)]+12+sin2x=(sinx+sin2x)31+sin2x=1+12+sin2x=sin2x

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