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The number of solution of $\tan x+\sec x=2 \cos x$ in $[0,2 \pi)$ is
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Verified Answer
The correct answer is:
3
3
The given equation is $\tan x+\sec x=2 \cos x \Rightarrow \sin x+1=2 \cos ^2 x$
$$
\begin{aligned}
& \Rightarrow \sin x+1=2\left(1-\sin ^2 x\right) \Rightarrow 2 \sin ^2 x+\sin x-1=0 \\
& \Rightarrow(2 \sin x-1)(\sin x+1)=0 \Rightarrow \sin x=\frac{1}{2},-1 \Rightarrow x=30^{\circ}, 150^{\circ}, 270^{\circ}
\end{aligned}
$$
$$
\begin{aligned}
& \Rightarrow \sin x+1=2\left(1-\sin ^2 x\right) \Rightarrow 2 \sin ^2 x+\sin x-1=0 \\
& \Rightarrow(2 \sin x-1)(\sin x+1)=0 \Rightarrow \sin x=\frac{1}{2},-1 \Rightarrow x=30^{\circ}, 150^{\circ}, 270^{\circ}
\end{aligned}
$$
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