Question

# The number of solutions of $$\tan x+\sec x= 2\cos x$$ in $$\left [ 0,2\pi \right ]$$ is

A
2
B
3
C
0
D
1

Solution

## The correct option is B 3$$\tan x+\sec x= 2 \cos x$$$$\Rightarrow 1+\sin x= 2\cos^{2}x$$$$\Rightarrow 1+ \sin x = 2\left ( 1- \sin^{2}x \right )$$$$\Rightarrow 2 \sin^{2}x +\sin x-1= 0$$$$\Rightarrow \left ( 2\sin x- 1 \right ) \left ( 1+\sin x \right )= 0$$$$\Rightarrow \sin x= \displaystyle \frac{1}{2}, \sin x= -1$$So there are three solutions like $$x=30^{0}, 150^{0}, 270^{0}$$Maths

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