Question

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

• A. $\frac {1}{\sqrt {3}}$
• B. $\sqrt {3}$
• C. $\frac {1}{2}$
• D. $1$

Answer 1

Answer: (B)

$\frac {\sin 70^\circ\, +\cos 40^\circ} {\cos 70^\circ + \sin 40^\circ}$
$=\frac{sin\, \left(90^{\circ}-20^{\circ}\right)+sin\,\left(90^{\circ}-40^{\circ}\right)}{cos\,\left(90^{\circ}-20^{\circ}\right)+sin\,\left(90^{\circ}-50^{\circ}\right)}$
$=\frac{cos\,20^{\circ}+cos\,40^{\circ}}{cos\,70^{\circ}+cos\,50^{\circ}}$
$=\frac{2\,cos\,30^{\circ}\,cos\,10^{\circ}}{2\,cos\,60^{\circ}\,cos\,10^{\circ}}=\frac{2\,cos\,30^{\circ}}{2\,cos\,60^{\circ}}$
$=\frac{2\left(\sqrt{3}/2\right)}{2\left(\frac{1}{2}\right)}=\sqrt{3}$