Chapter 13.2, Problem 30PPS

To determine

To Prove: The value of $\frac{\text{sec}\theta -\mathrm{cosec}\theta }{\mathrm{cosec}\theta \sec \theta }=\sin \theta -\cos \theta$

Explanation of Solution

Given information :

We know that, to prove the equation is $LHS=\frac{\sec \theta -\mathrm{cosec}\theta }{\mathrm{cosec}\theta \sec \theta }$

Proof :

  $\frac{\sec \theta -\mathrm{cosec}\theta }{\begin{array}{l}\mathrm{cosec}\theta \sec \theta \\ =\frac{\sec \theta }{\mathrm{cosec}\theta \sec \theta }-\frac{\mathrm{cosec}\theta }{\mathrm{cosec}\theta \sec \theta }\\ =\frac{1}{\mathrm{cosec}\theta }-\frac{1}{\sec \theta }\\ =\sin \theta -\cos \theta =RHS\end{array}}$