Question

How do you simplify `f(theta)=csc4theta-2cot2theta+5sec2theta` to trigonometric functions of a unit `theta`?

Answer 1

`f(theta)=csc4theta-2cot2theta+5sec2theta`

`=1/(sin4theta)-(2cos2theta)/(sin2theta)+5/(cos2theta)`

`=1/(2sin2thetacos2theta)-(2cos2theta)/(sin2theta)+5/(cos2theta)`

`=(1-4cos^2 2theta+10sin2theta)/(2sin2thetacos2theta)`

`=(1-4(2cos^2 theta-1)^2+20sinthetacostheta)/(4sinthetacostheta(2cos^2theta-1))`