Number of solutions of the equation tanx+secx=2cosx in the interval [0,2π] is

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

A
0
B
1
C
2
D
3

Solution:

$\frac{\sin x + 1}{\cos x} = 2 \cos x (\cos x \neq 0)$

$\Rightarrow 2 \sin^{2} x + \sin x - 1 = 0$

$\Rightarrow (2 \sin x - 1) (\sin x + 1) = 0$ , $\Rightarrow \sin x = \frac{1}{2}$

but $\sin x + 1 \neq 0 ∵ \cos x \neq 0)$

$\Rightarrow x = \frac{π}{6}, \frac{5 π}{6}$ in $[0, 2 π]$

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