Question

I need help with this Trig Identity with steps please 1+cot^3x/1+cotx=cscx^2-cotx

Answer 1

treat cot x as A, and it forms the form of B^3 + A^3 = ..., your B =1 , the same. just open and get the answer

Answer 2

$$\bf
\cfrac{1+cot^3(x)}{1+cot(x)}=csc^2(x)-cot(x)\\
\text{as already suggested by Loser66}\\
a^3+b^3 = (a+b)(a^2-ab+b^2)\\
1+cot^3(x) \implies 1^3 + cot^3(x)\\
\cfrac{1+cot^3(x)}{1+cot(x)} \implies
\cfrac{\cancel{(1+cot(x))}(1^2-(1)cot(x) +cot^2(x)) }{\cancel{1+cot(x)}}
$$

what does that leave you with?