Use the fundamental identities to fully simplify the expression.

Question

cot(x) cos(x) + csc(x) sin²(x)

Answer 1

cot(x)cos(x) + csc(x)sin²(x)

= [cos(x)/sin(x)]cos(x) + [1/sin(x)]sin²(x) <-- Quotient Identity and Reciprocal Identity

= cos²(x)/sin(x) + sin²(x)/sin(x)

= [cos²(x)+sin²(x)]/sin(x)

= 1/sin(x) <-- Pythagorean Identity

= csc(x) <-- Quotient Identity

Hope this helped!