The number of solution of $ an x+\sec x=2 \cos x$ in $[0,2 \pi)$ is

Question

The number of solution of $	an x+\sec x=2 \cos x$ in $[0,2 \pi)$ is

Aicharya · Accepted Answer

The given equation is $	an x+\sec x=2 \cos x \Rightarrow \sin x+1=2 \cos ^2 x$ $ \begin{aligned} & \Rightarrow \sin x+1=2\left(1-\sin ^2 xight) \Rightarrow 2 \sin ^2 x+\sin x-1=0 \ & \Rightarrow(2 \sin x-1)(\sin x+1)=0 \Rightarrow \sin x=\frac{1}{2},-1 \Rightarrow x=30^{\circ}, 150^{\circ}, 270^{\circ} \end{aligned} $

The number of solution of $\tan x+\sec x=2 \cos x$ in $[0,2 \pi)$ is

Solution