Question

How do you simplify `1/csc^2 x + (1/tan x)(cot x) + cos^2 x`?

Answer 1

Given Expression = `1/csc ^ 2 x + cot x / tan x + cos ^2 X`

= `sin ^ 2 x` + `cos ^ 2 x` + `cot ^ 2 x`
= 1 + `cot ^2 x`
= `csc ^ 2 x`

Explanation:

Note : I have used the formulae: `sin^2 x + cos ^2 x` = 1,
1/ tan x = cot x
and `1 + cot^ 2 x` = `csc ^2 x`, in the process of simplification.