Question:
The value of tan 75°– cot 75° is equal to
A. 2√3
B. 2 + √3
C. 2 – √3
D. 1
Solution:
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.