Question

prove that sec +tan = cos/1-sin​

Answer 1

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

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

→ $\sf{\frac{(1 + sin \theta)}{cos \theta} \times \frac{(1-sin \theta)}{(1- sin \theta)}}$

→ $\sf{\frac{(1 -sin² \theta)}{cos \theta(1-sin \theta)}}$

→ $\sf{\frac{cos² \theta}{cos \theta(1-sin \theta)}}$

→ $\sf{\frac{cos \theta}{1-sin \theta}}$

$\red{\tt{Hence \: Proved}}$