Question

Verify the identity. Show your work. cot^2x + csc^2x = 2csc^2x - 1

Answer 1

$\bf \textit{Pythagorean Identities} \\\\ 1+cot^2(\theta)=csc^2(\theta)\implies cot^2(\theta)=csc^2(\theta)-1\\\\ -------------------------------\\\\ cot^2(x)+csc^2(x)=2csc^2(x)-1 \\\\\\ \stackrel{\textit{doing the left-hand-side}}{\boxed{csc^2(x)-1}+csc^2(x)}\implies 2csc^2(x)-1$