Chapter 14.2, Problem 20PPS

To determine

To Verify : The value of $\frac{1+\tan \theta }{\sin \theta +\cos \theta }=\sec \theta$

Explanation of Solution

Given information :

We know that, the given equation is $\begin{array}{l}\frac{1+\tan \theta }{\sin \theta +\cos \theta }(L.H.S.)\\ \sec \theta (R.H.S.)\end{array}$

Formula Used:

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

Proof :

  $\begin{array}{l}L.H.S.\frac{1+\tan \theta }{\sin \theta +\cos \theta }=\frac{1+\frac{\sin \theta }{\cos \theta }}{\sin \theta +\cos \theta }\\ \left(\frac{\cos \theta +\sin \theta }{\sin \theta +\cos \theta }\right)\frac{1}{\cos \theta }=\frac{1}{\cos \theta }=\sec \theta =R.H.S.\end{array}$