Question

State whether the following relation is True or False:

${\tan }^2\theta +{\cos }^2\theta =1$

• A. True
• B. False

Answer 1

The correct option is B False

Given ${\tan }^2\theta +{\cos }^2\theta =1$

$R.H.S.$ can be written as:

$1={\sin }^2\theta +{\cos }^2\theta$

Let us assume given identity is true

Now equate $L.H.S.$ with $R.H.S.$

${\tan }^2\theta +{\cos }^2\theta ={\sin }^2\theta +{\cos }^2\theta$

${\tan }^2\theta ={\cos }^2\theta$

This is true only at $\theta =n\pi$