Q. The number of solutions of the equation $\tan{x + \sec{x = 2\cos x}}$ and $\cos{x \neq 0}$ lying in the interval $(0,\ 2\pi)$ is
A) 2
B) 1
C) 0
D) 3
Explanation
(a)
Given, $\tan{x + \sec{x = 2\cos x}}$
$\Rightarrow 1 + \sin{x = 2 - 2\sin^{2}x}$
$\Rightarrow \ \ \left( 2\sin{x - 1} \right)\left( \sin{x + 1} \right) = 0$
$\Rightarrow \ \sin{x = - 1,\frac{1}{2}}$
$\Rightarrow \ \ x = \frac{\pi}{6},\frac{5\pi}{6},\frac{3\pi}{2}$
But at $x = \frac{3\pi}{2}$ given equation does not exist
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.