Question

State true or false.

$\frac{\sin \theta .\cos \theta +1}{\sin \theta +\cos \theta -1}=\sec \theta +\tan \theta$

• A. True
• B. False

Answer 1

The correct option is A True

Given

LHS

$\frac{\sin \theta -\cos \theta +1}{\sin \theta +\cos \theta -1}$

Dividing Numerator and Denominator by $\cos \theta$

$⟹\frac{\tan \theta +\sec \theta -1}{\tan \theta -\sec \theta +1}$

$⟹\frac{\tan \theta +\sec \theta -({\sec }^2\theta -{\tan }^2\theta )}{\tan \theta -\sec \theta +1}$

$⟹\frac{\tan \theta +\sec \theta -(\sec \theta -\tan \theta )(\sec \theta +\tan \theta )}{\tan \theta -\sec \theta +1}$

$⟹\frac{\tan \theta +\sec \theta -(\sec \theta -\tan \theta )(\sec \theta +\tan \theta )}{\tan \theta -\sec \theta +1}$

$⟹\frac{\tan \theta +\sec \theta (\tan \theta -\sec \theta +1)}{\tan \theta -\sec \theta +1}$

$⟹\sec \theta +\tan \theta$