Question

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

Answer 1

$\frac{cot^{2} x}{1 + csc x}+ sin x * csc x = \\ = \frac{ \frac{cos ^{2} x}{sin ^{2} x} }{1+ \frac{1}{sin x} }+ sin x * \frac{1}{sin x}= \\ = \frac{ \frac{cos^{2} x}{sin ^{2} x} }{ \frac{sin x + 1}{sin x} }+ 1 = \\ = \frac{cos ^{2} x}{sin x ( sin x + 1 )}+ 1 = \\ = \frac{cos ^{2} x+sin x ( sin x + 1 )}{sin x ( sin x + 1 )}= \\ = \frac{cos ^{2} x+sin ^{2}x+ sin x }{sin x( sin x + )}= \\ = \frac{sinx+1}{sinx( sinx+1)} = \frac{1}{sin x}= csc x$