Question

Solve:
$\tan \theta +\csc \theta =\sec \theta$

Answer 1

$\begin{array}{c}\tan \theta +\cos ec\theta =\sec \theta \\ \Rightarrow \frac{\sin \theta }{\cos \theta }=\frac{1}{{\sin }^2\theta }\\ \Rightarrow \frac{{\sin }^2\theta +\cos \theta }{\sin \theta .\cos \theta }\\ \Rightarrow \frac{1-{\cos }^2\theta +\cos \theta }{\sin \theta .\cos \theta }=\frac{1+\cos \theta -{\cos }^2\theta }{\sin \theta .\cos \theta }Ans.\end{array}$