Question

The number of roots of the equation, $\cot x=\frac{\pi }{2}+x$ in $[-\pi ,\frac{3\pi }{2}]$ is,

• A. $3$
• B. $2$
• C. $1$
• D. infinite

Answer 1

The correct option is C $1$

we can see that $\cot x=\frac{\pi }{2}+x$

holds true for $x=\frac{-\pi }{2}$

as $\cot \frac{-\pi }{2}=\frac{\pi }{2}+\frac{-\pi }{2}\Rightarrow 0=0$

Therefore, Answer is $1$