Answer:
Rewrite [tex]csc^4x-cot^4x[/tex] by applying exponent rule [tex]a^{bc}=(a^b)^c[/tex]:
[tex]\implies (csc^2x)^2-(cot^2x)^2[/tex]
Apply difference of two squares formula [tex]x^2-y^2=(x+y)(x-y)[/tex]:
[tex]\implies (csc^2x+cot^2x)(csc^2x-cot^2x)[/tex]
Using trig identity [tex]1+cot^2x=csc^2x \implies 1=csc^2x-cot^2x[/tex]
[tex]\implies (csc^2x+cot^2x)(1)[/tex]
[tex]\implies csc^2x+cot^2x[/tex]
