Question

Number of solutions of the equation tan x + sec x = 2 cos x lying in the interval [0, 2$\pi$] is

• A. 1
• B. 2
• C. 3

Answer 1

The correct option is B 2

The given equation can be written as
$\frac{1+sinx}{cosx}=2cosx$
$\Rightarrow 1+sinx=2co{s}^{2}x=2(1-si{n}^2)x$
$\Rightarrow 2si{n}^{2}x+sinx-1=0$
$\Rightarrow (1+sinx)(2sinx-1)=0$
$\Rightarrow sinx=-1or\frac{1}{2}$
Now $sinx=-1\Rightarrow tanx$ and sec x not defined. $Sinx=\frac{1}{2}\Rightarrow x=\frac{\pi }{6}or\frac{5\pi }{6}$.
$\therefore$ The required number of solution is 2.