Question

The value of $\cos {12}^{\circ }+\cos {84}^{\circ }+\cos {132}^{\circ }+\cos {156}^{\circ }$ is

• A. $1$
• B. $\frac{1}{2}$
• C. $-\frac{1}{2}$
• D. $\frac{1}{4}$

Answer 1

Answer: (C)

$-\frac{1}{2}$

$cos12°+cos84°+cos156°+cos132°$

$=(cos12°+cos132°)+(cos84°+cos156°)$

$=2cos72°cos60°+2cos120°cos36°$

$=cos72°—cos36°=sin18°—cos36°$

$=-1/2$