Question

Expand
sin4  cos2 
in a series of cosines of
multiple of  .

Answer 1

Answer:

Then use the double angle formula derived by cos(2θ)=cos2(θ)−sin2(θ)=1−2sin2(θ)cos⁡(2θ)=cos2⁡(θ)−sin2⁡(θ)=1−2sin2⁡(θ) so

sin2(θ)=12⋅(1−cos(2θ))

sin2⁡(θ)=12⋅(1−cos⁡(2θ))

and you now plug into the factors of sin4(θ)sin4⁡(θ), and use the double angle formula for cos2(2θ)cos2⁡(2θ) to get the required answer.

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