Question

The value of $\frac{\tan {15}^{\circ }}{\cot {75}^{\circ }}$ is

• A. $\cos {90}^{\circ }$
• B. $\sin {30}^{\circ }$
• C. $\tan {45}^{\circ }$
• D. $\text{cosec}{75}^{\circ }$

Answer 1

The correct option is C $\tan {45}^{\circ }$

$\tan {15}^{\circ }=\tan (90-{75}^{\circ })=\cot {75}^{\circ }$

$\therefore \frac{\tan {15}^{\circ }}{\cot {75}^{\circ }}=\frac{\cot 75}{\cot 75}=\tan 45=1$