Question

How do you simplify `f(theta)=csc2theta-cos4theta-3cot2theta` to trigonometric functions of a unit `theta`?

Answer 1

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

Explanation:

`csc 2x = 1/(sin 2x) = 1/(2sin x.cos x)` (1)

`-cos 4x = -(1 - 2sin^2 2x) = -(1 - sqrt2sin 2x)(1 + sqrt2sin 2x) =`
`= -(1 - 2sqrt2sin x.cos x)(1 + 2sqrt2sin x.cos x)` (2)

`-3cot 2x = - 3/(tan 2x) = - (3(1 - tan^2 x))/(2tan x)` (3)

Ans: f(x) = (1) + (2 ) + (3)