Q.

If sinx+sin2x=1, then cos12x+3cos10x+3cos8x+cos6x-2 is equals to


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a

0

b

1

c

-1

d

2  

answer is C.

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Detailed Solution

Given that, sinx+sin2x=1.
 sinx=cos2x Now, we need to find the value of cos12x+3cos10x+3cos8x+cos6x-2.
=sin6x+3sin5x+3sin4x+sin3x-2
=(sin2x)3+3(sin2x)2sinx+3(sin2x)2+sin2xsinx-2 =(sin2x)3+3(sin2x)2sinx+3sin2x(sinx)2+sin3x-2 =(sin2x+sinx)3-2 =1-2
=-1 So, the value of cos12x+3cos10x+3cos8x+cos6x-2 is -1.
Hence, the correct option is (3).
 
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