Question

If sinθ + sin^2 θ = 1, find the value of :- cos^12 θ + 3 cos^10 θ + 3 cos^8 θ + cos^6 theta​

Answer 1

Step-by-step explanation:

Consider the given data.

sinθ+sin2θ=1

sinθ=1−sin2θ

sinθ=cos2θ

 

We have,

=cos12θ+3cos10θ+3cos8θ+cos6θ+2cos4θ+2cos2θ−2

=cos12θ+3cos10θ+3cos8θ+cos6θ+2(cos4θ+cos2θ−1)

=(cos4θ+cos2θ)3+2(cos4θ+cos2θ−1)

 

Since, sinθ=cos2θ

 

Therefore,

=(sin2θ+sinθ)3+2(sin2θ+sinθ−1)

=13+2(1−1)

=1+0

=1

 

Hence, the required value is