Question

How do you simplify `f(theta)=sin4theta-cos2theta` to trigonometric functions of a unit `theta`?

Answer 1

`4sinthetacos^3theta-cos^2theta-4sin^3thetacostheta+sin^2theta`

Explanation:

`f(theta)=2sin(2theta)cos(2theta)-cos(2theta)`

`f(theta)=cos(2theta)(2sin(2theta)-1)`

`f(theta)=(cos^2theta-sin^2theta)(2*2sinthetacostheta-1)`

`f(theta)=(cos^2theta-sin^2theta)(4sinthetacostheta-1)`

`4sinthetacos^3theta-cos^2theta-4sin^3thetacostheta+sin^2theta`