Question

Math Analysis: Simplify each expression.
(cot^2 x/1 + csc x) + sin x*csc x

Answer 1

`(cot^(2) x)/(1 + csc x)+ sin x * csc x = \\ = ( (cos ^(2) x)/(sin ^(2) x) )/(1+ (1)/(sin x) )+ sin x * (1)/(sin x)= \\ = ( (cos^(2) x)/(sin ^(2) x) )/( (sin x + 1)/(sin x) )+ 1 = \\ = (cos ^(2) x)/(sin x ( sin x + 1 ))+ 1 = \\ = (cos ^(2) x+sin x ( sin x + 1 ))/(sin x ( sin x + 1 ))= \\ = (cos ^(2) x+sin ^(2)x+ sin x )/(sin x( sin x + ))= \\ = (sinx+1)/(sinx( sinx+1)) = (1)/(sin x)= csc x`