Q. If $\cos{(\theta + \varnothing)} = mcos\ (\theta - \varnothing)$, then $\tan\theta$ is equal to
A) $\lbrack(1 + m)/(1 - m)\rbrack\tan\ \varnothing$
B) $\lbrack(1 - m)/(1 + m)\rbrack\tan\ \varnothing$
C) $\lbrack(1 - m)/(1 + m)\rbrack\cot\ \varnothing$
D) $\lbrack(1 + m)/(1 - m)\rbrack\sec\ \varnothing$
Explanation
(c)
$\cos{(\theta + \phi)} = mcos\ (\theta - \phi)$
$\Rightarrow \cos{\theta\cos{\phi - \sin{\theta\sin{\phi = m\cos{\theta\cos{\phi + m\sin{\theta\sin\phi}}}}}}}$
$\Rightarrow \ \ \cos{\theta\cos{\phi\ (1 - m) = \sin{\theta\sin{\phi(1 + m)}}}}$
$\Rightarrow \tan{\theta = \left\lbrack \frac{1 - m}{1 + m} \right\rbrack}\cot\phi$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.