Number of solutions of the trigonometric equation $2 an 2 heta-\cot 2 heta+1=0$ lying in the interval $[0, \pi]$ is

Question

Number of solutions of the trigonometric equation $2 	an 2 	heta-\cot 2 	heta+1=0$ lying in the interval $[0, \pi]$ is

Aicharya · Accepted Answer

$\begin{aligned} & 	ext { } 2 	an 2 	heta-\cot 2 	heta+1=0 \ & 	ext { Let } 	an 2 	heta=x \Rightarrow 2 x-\frac{1}{x}+1=0 \ & \Rightarrow 2 x^2+x-1=0 \Rightarrow x=-1, \frac{1}{2} \ & \Rightarrow 	an 2 	heta=-1, \frac{1}{2}\end{aligned}$ $	herefore$ Required number of solutions are 4.

Number of solutions of the trigonometric equation $2 \tan 2 \theta-\cot 2 \theta+1=0$ lying in the interval…

Solution