The value of tan 75°– cot 75°

A. 2√3

Explanation:

According to the question,

We have,

tan 75°– cot 75°

$=\frac{\sin 75^{\circ}}{\cos 75^{\circ}}-\frac{\cos 75^{\circ}}{\sin 75^{\circ}}$

$=\frac{\sin ^{2} 75^{\circ}-\cos ^{2} 75^{\circ}}{\cos 75^{\circ} \sin 75^{\circ}}$

$=\frac{2\left(\sin ^{2} 75^{\circ}-\cos ^{2} 75^{\circ}\right)}{2 \cos 75^{\circ} \sin 75^{\circ}}$

$=\frac{-2 \cos 150^{\circ}}{\sin 150^{\circ}}$

= -2cot150°

= -2 cot (180°-30°)

= 2cot30°

=2√3

Thus, option (A) 2√3 is the correct answer.