The value of 75^ - 75^ is equal to: - Vidyadip

MCQ

The value of $\tan75^\circ-\cot75^\circ$ is equal to:

✓
$2\sqrt{3}$
B
$2+\sqrt{3}$
C
$2-\sqrt{3}$
D
$1$

✓

Answer

Correct option: A.

$2\sqrt{3}$

$\tan75^\circ-\cot75^\circ=\frac{\sin75^\circ}{\cos75^\circ}-\frac{\cos75^\circ}{\sin75^\circ}\\=\frac{2(\sin^275^\circ-\cos^275^\circ)}{2\sin75^\circ\cos75^\circ}=\frac{-2\cos150^\circ}{\sin150^\circ}$
$=-2\cot150^\circ$
$=-2\cot(180^\circ-30^\circ)$
$=2\cot30^\circ$
$=2\sqrt3$

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