Question

If $\frac{\sin \theta }{\cos \theta }+\frac{\cos \theta }{\sin \theta }=2$ with $0<\theta <{90}^{\circ }$ then what is $\theta$ equal to?

• A. ${30}^{\circ }$
• B. ${45}^{\circ }$
• C. ${60}^{\circ }$
• D. ${75}^{\circ }$

Answer 1

The correct option is B ${45}^{\circ }$

$\tan \theta +\cot \theta =2,0<\theta <{90}^{\circ }$
We know $1+1=2$
and $\tan {45}^{\circ }=\cot {45}^{\circ }=1$
$\therefore \theta ={45}^{\circ }$