Question

Verify the identity. Show your work. cot2x + csc2x = 2csc2x - 1

Answer 1

\cot^2 x + \csc^2 x \implies \frac{\cos^2 x} {\sin^2 x} + \frac{1}{\sin^2 x} \implies \frac{\cos^2 x +1}{\sin^2 x} \implies \frac{1- \sin^2 x + 1}{\sin^2 x} \implies \frac{2 - \sin^2 x}{\sin^2 x} \implies \frac{2}{\sin^2 x} - \frac{\sin^2 x}{\sin^2 x} \implies 2 \csc^2 x - 1