Question

The total number of solutions of $\tan x+\cot x=2\cos ecx$ in $[-2\pi ,\pi ]$ is

• A. $2$
• B. $3$
• C. $4$
• D. $7$

Answer 1

Answer: (B)

$3$

$tanx+cotx=2cscx$

$\Rightarrow \frac{sinx}{cosx}+\frac{cosx}{sinx}=\frac{2}{sinx}$

$\Rightarrow \frac{(si{n}^{2}x+co{s}^{2}x)}{(cosx.sinx)}=\frac{2}{sinx}$

$\Rightarrow cosx=\frac{1}{2}$, since $sinx\ne 0$ in domain

Thus, solution in the given interval is,

$x=\frac{-5\pi }{3},\frac{-\pi }{3},\frac{\pi }{3}$