70^ + 40^ 70^ + 40^ = - Vidyadip

MCQ

$\frac{\sin 70^{\circ}+\cos 40^{\circ}}{\cos 70^{\circ}+\sin 40^{\circ}}=$

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

✓

Answer

Correct option: B.

$\sqrt{3}$

(B)
$\frac{\sin 70^{\circ}+\cos 40^{\circ}}{\cos 70^{\circ}+\sin 40^{\circ}}=\frac{\sin 70^{\circ}+\sin 50^{\circ}}{\cos 70^{\circ}+\cos 50^{\circ}}$
$=\frac{2 \sin 60^{\circ} \cos 10^{\circ}}{2 \cos 60^{\circ} \cos 10^{\circ}}$
$=\tan 60^{\circ}$
$=\sqrt{3}$

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