Question

How do you simplify `f(theta)=tan2theta-2cot2theta-csc2theta` to trigonometric functions of a unit `theta`?

Answer 1

f(x) = tan 2x - 2cot 2x - csc 2x

Explanation:

`tan 2x = (2tan x)/(1- tan^2 x)` (1)
`-2cot 2x = - 2/(tan 2x) = - (1 - tan^2 x)/tan x` (2)
`- csc 2x = - 1/(sin 2x) = - 1/(2sin x.cos x)` (3)
Finally,

f(x) = (1) + (2) + (3).