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Question

If sin2x+sinx1=0, then the value of cos12x+3cos10x+3cos8x+cos6x is

A
1
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B
8
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C
1
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D
8
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Solution

The correct option is A 1
Let I=cos12x+3cos10x+3cos8x+cos6x
I=(cos4x)3+3cos6x(cos4x+cos2x)+(cos2x)3I=(cos4x+cos2x)3

Now, sin2x+sinx1=0
sinx=1sin2xsinx=cos2x (1)sin2x=cos4x (2)

From (1) and (2),
I=(sin2x+sinx)3I=1

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