Question

How do you simplify `-sin4theta-cos2theta+sin^2theta` to trigonometric functions of a unit `theta`?

Answer 1

We have that

`sin(4theta)=2sin(2theta)*cos(2theta)=2*sin(theta)*cos(theta)(cos^2(theta)-sin^2(theta))`

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

Hence

`-sin(4theta)-cos(2theta)+sin^2(theta)=-2*sin(theta)*cos(theta)(cos^2(theta)-sin^2(theta))-(cos^2(theta)-sin^2(theta))+sin^2theta`