Question

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

• A. 1
• B. 2
• C. 3

Answer 1

The correct option is B 2

The given equation can be written as $\frac{sinx+1}{cosx}=2cosx\Rightarrow sinx+1=2co{s}^{2}x(cosx\ne 0)\Rightarrow 2si{n}^{2}x+sinx-1=0\Rightarrow (2sinx-1)(2sinx+1)=0\Rightarrow sinx=\frac{1}{2}(\because sinx+1\ne 0ascosx\ne 0)\Rightarrow x=\frac{\pi }{6},\frac{5\pi }{6}in[0,2\pi ]$. The required number of solutions is 2.