Question

Establish each identity: sin θ (cot θ + tan θ) = sec θ

Answer 1

Taking LHS
\[\sin \theta(\frac{\cos \theta}{\sin \theta}+\frac{\sin \theta}{\cos \theta})\]
take LCM,
\[\sin \theta(\frac{(\cos \theta)^{2}+(\sin \theta)^{2}}{\sin \theta\cos \theta})\]
\[\cancel\sin \theta(\frac{1}{\cancel\sin \theta\cos \theta})\]