Question

How do you use the double angle or half angle formulas to simplify `f(θ) = (cos θ − 3 sin θ)^2`?

Answer 1

`f(theta)=(costheta-3sintheta)^2`

`=cos^2theta-6sinthetacostheta+9sin^2theta`

`=1/2(1+cos2theta)-3sin2theta+9/2(1-cos2theta)`

`=5-4cos2theta-3sin2theta`