Question

$\frac{\left(1+\sin \theta \right)\left(1-\sin \theta \right)}{\cos ec\theta -\cot \theta \cos ec\theta +\cot \theta }=\left(1+\cot \theta \right)$

• A. True
• B. False

Answer 1

The correct option is B False

$\frac{(1+\sin \theta )(1-\sin \theta )}{\csc \theta -\cot \theta \csc \theta +\cot \theta }$

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

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

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