Question

5.
If sin x+sin ^2 x=1, then the value of cos 12 x+3 cos ^10 x + 3 cos^8 x + cos^6 x-2 is equal to:
a) 0
b) 1
c) -1
d] 2​

Answer 1

sinx+sin2x=1

or,sinx=1−sin2x=cos2x

or,sin2x=cos4x

cos12x+3cos10x+3cos8x+cos6x

=cos6x(cos6x+3cos4x+3cos2x+1)

=cos6x((cos2x)3+3(cos2x)2.1+3.cos2x.12+1)  

=(cos2x)3(cos2x+1)3

=(cos4x+cos2x)3

=(sin2x+cos2x)3

=13

=1

So, the answer is (b) 1.