Question

Number of solutions of the equation $\tan x + \sec x = 2\cos x$ lying in the interval [0. 2π] is

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

Answer: (C)

2

Answer 2

The given equation can be written as $\frac{\sin x + 1}{\cos x} = 2\cos x$

⇒ $\sin x + 1 = 2\cos^{2}x\left( \cos x \neq 0 \right)$

⇒ $2\sin^{2}x + \sin x - 1 = 0$

⇒ $\left( 2\sin x - 1 \right)\left( \sin x + 1 \right) = 0$

⇒ $\sin x = \frac{1}{2}$ $\left( \because\sin x + 1 \neq 0\text{ as cosx} \neq 0 \right)$

⇒ $x = \frac{\pi}{6},\frac{5\pi}{6}$in $\lbrack 0,2\pi\rbrack$ so that required number of solutions is 2.