Question

How can you solve `csc^4 x − co^t4 x = csc^2 x + cot^2 x` ?

Answer 1

Please see below.

Explanation:

Let us use the identity `a^2-b^2=(a-b)(a_b)`

`csc^4x-cot^4x`

= `(csc^2x)^2-(cot^2x)^2`

= `(csc^2x-cot^2x)(csc^2x+cot^2x)`

= `1xx(csc^2x+cot^2x)` - as `csc^2x=1+cot^2x`

= `csc^2x+cot^2x`