Question

The total number of solutions of tanx+cotx=2cosecx in $[-2\pi ,2\pi ]$ is equal to.

• A. 7
• B. 6
• C. 4
• D. 2

Answer 1

The correct option is C 4

$tanx+cotx=2cosecx\frac{sinx}{cosx}+\frac{cosx}{sinx}=\frac{2}{sinx}\Rightarrow \frac{1}{sinx.cosx}=\frac{2}{sinx}\Rightarrow sinx\ne 0\Rightarrow cosx=\frac{1}{2}\therefore x=\pm \frac{\pi }{3},\pm \frac{5\pi }{3}$