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

(B) False.
$L$.$H$.$S$. $= (\tan \theta + 2)(2 \tan \theta + 1)$
$= 2 \tan^2 \theta + \tan \theta + 4 \tan \theta + 2$
$= 2 \tan^2 \theta + 5 \tan \theta + 2$
Using the identity $\tan^2 \theta = \sec^2 \theta - 1$:
$= 2(\sec^2 \theta - 1) + 5 \tan \theta + 2$
$= 2 \sec^2 \theta - 2 + 5 \tan \theta + 2$
$= 2 \sec^2 \theta + 5 \tan \theta$
Since $2 \sec^2 \theta + 5 \tan \theta \neq 5 \tan \theta + \sec^2 \theta$,the given statement is False.