(sin^2x)(1+cot^2x)=1

Question

Verify the Identity. 

Answer 1

Note that         1 + cot²x = csc²x

 

Then, working the left side,

 

(sin²x)(csc²x) =

sin²x / sin²x = 1

Answer 2

sin²x (1 + cot²x) = sin²x(1 + cos²x/sin²x) = sin²x + cos²x = 1