Question

State whether the following statement is true or false.

$\frac{1+\cos \theta -{\sin }^2\theta }{\sin \theta (1+\cos \theta )}=\cot \theta$

• A. True
• B. False

Answer 1

The correct option is A True

$\frac{1+\cos \theta -{\sin }^2\theta }{\sin \theta (1+\cos \theta )}=\cot \theta$

$\Rightarrow$ $L.H.S=\frac{1+\cos \theta -{\sin }^2\theta }{\sin \theta (1+\cos \theta )}$

$=\frac{1+\cos \theta -(1-{\cos }^2\theta )}{\sin \theta (1+\cos \theta )}$

$=\frac{1+\cos \theta -1+{\cos }^2\theta }{\sin \theta (1+\cos \theta )}$

$=\frac{\cos \theta +{\cos }^2\theta }{\sin \theta (1+\cos \theta }$

$=\frac{\cos \theta (1+\cos \theta )}{\sin \theta (1+\cos \theta )}$

$=\frac{\cos \theta }{\sin \theta }$

$=\cot \theta$

$=R.H.S$