Question

find whether ${(\sin \theta +co\sec \theta )}^2+{(\cos \theta +\sec \theta )}^2=7+{\tan }^2\theta +{\cos }^2\theta$ is true or false.

• A. True
• B. False

Answer 1

The correct option is B False

$LHS=(\sin \theta +\text{cosec}\theta {)}^2+(\cos \theta +\text{sec}\theta {)}^2$

$={\sin }^2\theta +{\text{cosec}}^2\theta +2\sin \theta \text{cosec}\theta +{\cos }^2\theta +{\text{sec}}^2\theta +2\cos \theta \text{sec}\theta$

$=({\sin }^2\theta +{\cos }^2\theta )+1+{\cot }^2\theta +2+1+{\tan }^2\theta +2$

$=7+{\tan }^2\theta +{\cot }^2\theta \ne RHS$

So the relation is $\text{False}$