Question

If $2\sec \theta \text{cosec}\theta -\cot \theta =3$, then the value of $\tan \theta$ is/are

• A. $1$
• B. $\frac{1}{2}$
• C. $\frac{1}{3}$
• D. $\frac{1}{4}$

Answer 1

Answer: (A), (B)

The correct options are
A $1$
B $\frac{1}{2}$

$2\sec \theta \text{cosec}\theta -\cot \theta =3$
Dividing the equation by $\cot \theta$,
$\Rightarrow 2{\sec }^2\theta -1=3\tan \theta$
$\Rightarrow 2(1+{\tan }^2\theta )-1=3\tan \theta$
$\Rightarrow 2{\tan }^2\theta -3\tan \theta +1=0\Rightarrow (2\tan \theta -1)(\tan \theta -1)=0$
$\Rightarrow \tan \theta =1,\frac{1}{2}$