Question

How do you simplify `f(theta)=csc2theta-sec2theta-3cot2theta` to trigonometric functions of a unit `theta`?

Answer 1

`f(theta)=1/(sin(2theta))=1/(2sinthetacostheta)-1/(2cos^2theta-1)-(2-1tan^2theta)/(2tantheta)`

Explanation:

Break the function down by term:
`csc(2theta)=1/(sin(2theta))=1/(2sinthetacostheta)`

`sec(2theta)=1/(cos(2theta))=1/(cos^2theta-sin^2theta)=1/(2cos^2theta-1)`

`cot(2theta)=1/tan(2theta)=(1-tan^2theta)/(2tantheta)`

Put this hell together:

`f(theta)=1/(sin(2theta))=1/(2sinthetacostheta)-1/(2cos^2theta-1)-(3-3tan^2theta)/(2tantheta)`