Simplify sin^2(x)+sin^2(x)cot^2(x)

Question

Help please, I am stuck and need clarification. Total brain fart, so work shown would really help.

Answer 1

cot(x) is defined as cos(x)/sin(x). 

 

Based on this,   sin²⁽x) + sin²⁽x)cot²⁽x) = sin²⁽x) + cos²⁽x) = 1

 

So the expression is equal to 1.

Answer 2

sin²x+sin²xcot²x = sin²x(1+cot²x)    (1+cot²x=csc²x)

                                                   

                          =sin²x.csc²x

 

                          =sin²x. 1

                                    sin²x

                           = 1