Question

Verify identity
cot^2x + csc^2x = 2csc^2x - 1

Answer 1

\[\cot^2 x + \csc^2 x\]
\[\implies \frac{\cos^2 x} {\sin^2 x} + \frac{1}{\sin^2 x}\]
\[\implies \frac{\cos^2 x +1}{\sin^2 x}\]
\[\implies \frac{1- \sin^2 x + 1}{\sin^2 x}\]
\[\implies \frac{2 - \sin^2 x}{\sin^2 x}\]
\[\implies \frac{2}{\sin^2 x} - \frac{\sin^2 x}{\sin^2 x}\]
\[\implies 2 \csc^2 x - 1\]
does that help?

Answer 2

thank u!

Answer 3

welcome :D