Question

for all values of x for which the expressions are defined, prove that the following is an identity: tanxcsc^2 x/1+tan^2 x=cotx

Answer 1

\[\frac{\frac{\sin x}{\cos x}\frac{1}{\sin ^2x}}{\sec ^2x}=\frac{\frac{1}{\sin x \cos x}}{\frac{1}{\cos ^2x}}=\frac{1}{\sin x \cos x}\times \cos ^2x=\frac{\cos x}{\sin x}=\cot x\]