Question

tan theta/1-cos squared theta = sec theta csc theta

Answer 1

\[\frac{ \tan(\theta) }{ 1-\cos^2(\theta) }=\sec(\theta)\csc(\theta)\]Let's solve the left side and make it look like the right side. If we can get it to be the same as the right side, then we have proved the identity.\[L.S=\frac{ \frac{ \sin(\theta) }{ \cos(\theta) } }{ \sin^2(\theta) }=\frac{ \sin(\theta) }{ \cos(\theta) }*\frac{ 1 }{ \sin^2(\theta) }=\frac{ 1 }{ \cos(\theta)\sin(\theta) }=\frac{ 1 }{ \cos(\theta) }*\frac{ 1 }{ \sin(\theta)}\]\[=\sec(\theta)\csc(\theta) \implies L.S = R.S\]
@AllieBakewell