Browse Questions

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

$(a)\;2\qquad (b)\;3\qquad(c)\;0\qquad(d)\;1$

The given equation is $\tan x+\sec x=2\cos x$
$\Rightarrow \sin x+1=2\cos^2x$
$\Rightarrow \sin x+1=2(1-\sin^2x)$
$\Rightarrow 2\sin^2x+\sin x-1=0$
$\Rightarrow (2\sin x-1)(\sin x+1)=0$