simplify the trigonometric expression

Question

(Cos^2x/sin^2x)+ cscxsinx

Answer 1

The given trigonometric expression is (cos^2x)/(sin^2x)+cscxsinx

= (cos^2x)/(sin^2x)+1/sinx(sinx)      [ since cscx = 1/sinx ]

= cot^2x+1                            [ cosx/sinx = cotx ]

Apply pythagorean identity 1+cot^2x = csc^2x

= csc^2x 

The solution is csc^2x.