1- 2^ 62^ 152^ - 88^ = - Vidyadip

MCQ

$\frac{1-\tan2^{\circ}\cot62^{\circ}}{\tan152^{\circ}-\cot88^{\circ}}=$

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

✓

Answer

Correct option: B.

$-\sqrt{3}$

(B)
$\frac{1-\tan2^{\circ}\cot62^{\circ}}{\tan152^{\circ}-\cot88^{\circ}}$
$=\frac{1-\tan2^{\circ}\cot62^{\circ}}{\tan\left(90^{\circ}+62^{\circ}\right)-\cot\left(90^{\circ}-2^{\circ}\right)}$
$=\frac{1-\tan2^{\circ}\cot62^{\circ}}{\cot62^{\circ}\tan2^{\circ}}$
$=\frac{\tan62^{\circ}-\tan2^{\circ}}{-\left(1+\tan2^{\circ}\tan62^{\circ}\right)}$
$=-\tan\left(62^{\circ}-2^{\circ}\right)$
$=-\tan60^{\circ}=-\sqrt{3}$

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