Question

The value of cos $^2 10^{\circ} - cos10^{\circ} cos50^{\circ} + cos^2 50^{\circ}$

• A. $\frac{3}{2}(1+cos 20^{\circ})$
• B. $\frac{3}{4}$
• C. $\frac{3}{4} + cos 20^{\circ}$
• D. $\frac{3}{2}$

Answer 1

Answer: (B)

$\frac{1}{2} (2 cos^2 10^{\circ} - 2 cos 10^{\circ} cos 50^{\circ} | + 2 cos^2 50^{\circ})$
$\Rightarrow \, \, \frac{1}{2} (1 + cos 20^{\circ}- (cos60^{\circ} + cos40^{\circ}) + 1 + cos100^{\circ})$
$\Rightarrow \, \, \frac{1}{2} \bigg(\frac{3}{2}+ cos 20^{\circ} + 2 sin 70^{\circ} sin (-30^{\circ})\bigg)$
$\Rightarrow \, \, \frac{1}{2} \bigg(\frac{3}{2} + cos 20^{\circ} - sin 70^{\circ}\bigg)$
$\Rightarrow \, \frac{3}{4}$