Question

$(\tan \theta +2)(2\tan \theta +1)=5\tan \theta +sec2\theta$. Write ‘True’ or ‘False’ and justify your answer.

• A. True
• B. False

Answer 1

The correct option is B False

Trigonometric identity:

$L.H.S.(\tan \theta +2)(2\tan \theta +1)$

$=2{\tan }^2\theta +\tan \theta +4\tan \theta +2$

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

$=2\left(se{c}^2\theta -1\right)+5\tan \theta +2\left[\because 1+{\tan }^2\theta ={\sec }^2\theta \right]$

$=2se{c}^2\theta -2+5\tan \theta +2$ $\mathbf{[}\mathbf{\because }\mathbf{1}\mathbf{+}{\mathbf{tan}}^{\mathbf{2}}\mathbf{\theta }\mathbf{=}{\mathbf{sec}}^{\mathbf{2}}\mathbf{\theta }\mathbf{]}$ $=2se{c}^2\theta +5\tan \theta$

$\ne R.H.S$

$\therefore L.H.S\ne R.H.S$

Hence, the given statement is false.