NIELIT 2022 Feb Scientist D - Section D: 8

Question

If $\{ (2 \sin \theta – \cos \theta) / (\cos \theta + \sin \theta) \} = 1,$ then the value of $\tan \theta$ is :

• A. $\frac{1}{3}$
• B. $\frac{1}{2}$
• C. $2$
• D. $3$

Answer 1

Given that:$\frac{2\sin \theta-\cos \theta}{\cos \theta+\sin \theta}=1$

$\implies2\sin \theta-\cos \theta=\cos \theta +\sin \theta$

$\implies \sin \theta=2\cos \theta$

$\implies \frac{\sin \theta}{\cos\theta}=2$

$\implies \tan \theta=2$

Option (C) is correct.