Write 'True' or 'False' and justify your answer in each of the following:
$ (\tan \theta+2)(2 \tan \theta+1)=5 \tan \theta+\sec ^{2} \theta $.

Given:

\( (\tan \theta+2)(2 \tan \theta+1)=5 \tan \theta+\sec ^{2} \theta \).

To do:

We have to find whether the given statement is true or false.

Solution:

We know that,

$\sec ^{2} \theta-\tan ^{2} \theta=1$

Therefore,

$(\tan \theta+2)(2 \tan \theta+1)=2 \tan ^{2} \theta+4 \tan \theta+\tan \theta+2 $

$=2(\sec ^{2} \theta-1)+5 \tan \theta+2$

$=2 \sec ^{2} \theta+5 \tan \theta$

The given statement is true.

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

24 Views

Kickstart Your Career

Get certified by completing the course

Get Started