Question

State of true or false$\frac{\tan \theta -\cot \theta }{\sin \theta \cos \theta }={\tan }^2\theta -{\cot }^2\theta$.

• A. True
• B. False

Answer 1

The correct option is A True

$\frac{\tan \theta -\cot \theta }{\sin \theta \cos \theta }=\frac{\frac{\sin \theta }{\cos \theta }-\frac{\cos \theta }{\sin \theta }}{\sin \theta \cos \theta }$

$=\frac{\sin \theta }{\sin \theta {\cos }^2\theta }-\frac{\cos \theta }{{\sin }^2\theta \cos \theta }$

$={\text{sec}}^2\theta -{\text{cosec}}^2\theta$

$=(1+{\tan }^2\theta )-(1+{\cot }^2\theta )$

$={\tan }^2\theta -{\cot }^2\theta$

So the relation is $\text{True}$