Question

Can anyone prove this?

Answer 1

Answer:

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 $1+cot^2x=csc^2x \implies 1=csc^2x-cot^2x$

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

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