Question

If $2 \, \sec \, 2 \theta = \tan \, \phi + \cot \, \phi ,$ then a value of $\theta + \phi$ is

• A. $\frac{\pi}{2}$
• B. $\frac{\pi}{4}$
• C. $\frac{\pi}{3}$
• D. $\pi$

Answer 1

Answer: (B)

Given $2 \sec2 \theta = \tan \phi+ \cot\phi $
$\Rightarrow 2 \sec2 \theta = 2 cosec 2 \phi $
$\Rightarrow \sec2\theta = cosec 2 \phi $
$\Rightarrow \sec2 \theta = \sec\left(\frac{\pi}{2} - 2 \phi\right)$
$ \Rightarrow 2\theta = \frac{\pi}{2} - 2 \phi$