Write ‘True’ or ‘False’ and justify your answer. ( +2)(2 +1)=5 + … - Vidyadip

Question

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

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Answer

False.LHS$=(\tan\theta+2)(2\tan\theta+1)$
$=\tan\theta(2\tan\theta+1)+2(2\tan\theta+1)$
$=2\tan^2\theta+\tan\theta+4\tan\theta+2$
$=2\tan^2\theta+5\tan\theta+2$
$=2(\tan^2\theta+1)+5\tan\theta$
$=2\sec^2\theta+5\tan\theta\neq$ RHS
Hence, the given statement is false.

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