Question

If cos theta+cos^(2)theta+cos^(3)theta=1 and sin^(6)theta=a+b sin^(2)theta+c sin^(4)theta then a+b+c=​

Answer 1

Answer:

Combining cosθ and cos3θ.

(cosθ+cos3θ)+cos2θ=0

2cos2θcosθ+cos2θ=0

or cos2θ(2cosθ+1)=0

∴cos2θ=0=cos(π/2),

∴2θ=(n+

2

1

)π,

or θ=(2n+1)π/4

2cosθ+1=0

∴cosθ=−1/2=−cos(π/3)

=cos(π−π/3)=cos(2π/3)

∴θ=2nπ±2π/3.