Question

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

• A. 2
• B. 3
• C. 0
• D. 1

Answer 1

The correct option is B 3

$\tan x+\sec x=2\cos x$

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

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

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

$\Rightarrow (2\sin x-1)(1+\sin x)=0$

$\Rightarrow \sin x=\frac{1}{2},\sin x=-1$

So there are three solutions like $x={30}^0,{150}^0,{270}^0$