Question

Can anyone prove this?

Answer 1

Rewrite
`csc^4x-cot^4x` by applying exponent rule
`a^(bc)=(a^b)^c`:

`\implies (csc^2x)^2-(cot^2x)^2`

Apply difference of two squares formula
`x^2-y^2=(x+y)(x-y)`:

`\implies (csc^2x+cot^2x)(csc^2x-cot^2x)`

Using trig identity
`1+cot^2x=csc^2x \implies 1=csc^2x-cot^2x`

`\implies (csc^2x+cot^2x)(1)`

`\implies csc^2x+cot^2x`