Sin^2 x question

Question

 

How do I prove that sin^2  x(1 + cot^2  x) = 1

 

 

thanks

Answer 1

sin²(x)[1 + cot²(x)] = 1

 

Identity: cot(x) = cos(x)/sin(x)

 

sin²(x)[1 + cos²(x)/sin²(x)] = 1

 

Distribute the sin²(x) across the terms in the brackets:

 

sin²(x) + cos²(x) = 1

 

which is a Pythagorean Identity.