Question

$Prove\:\csc ^2\left(θ\right)\tan ^2\left(θ\right)-1=\tan ^2\left(θ\right)$

Answer 1

\[\csc ^2\left(θ\right)\tan ^2\left(θ\right)-1=\tan ^2\left(θ\right)\]

Answer 2

\[\color{blue}{ \csc^2θ=\frac{1}{\sin^2θ} ~~~~~~~~and~~~~~~~~\tan^2θ=\frac{\sin^2θ}{\cos^2θ} }~~~~~~~~~~~~~~~~~So,\]\[\color{black}{ \frac{1}{\sin^2θ} \times \frac{\sin^2θ}{\cos^2θ} -1=\tan^2θ}\]\[\color{black}{ \frac{1}{\cos^2θ}-1=\tan^2θ}\]\[\color{black}{ \sec^2θ-1=\tan^2θ}\]\[\color{blue}{ Verified.~~~~~~~~\color{green}{✓}\color{red}{✓}\color{goldenrod}{✓}}\]