Question

The value of the expression, $\cos 35^{\circ }+\cos 125^{\circ }+$ $2\sin 185^{\circ }\left(\sin 130^{\circ }+\sin 140^{\circ }\right)$ is

• A. positive and greater than $(1/2)$
• B. negative and less than $(-1/2)$
• C. $1/2$
• D. $0$

Answer 1

Answer: (D)

$\cos 35^{\circ }+\cos 125^{\circ }+2\sin 185^{\circ }\left(\sin 130^{\circ }+\sin 140^{\circ }\right)$
$=2\cos 80^{\circ }\cos 45^{\circ }-2\sin 5^{\circ }\left(2\sin 135^{\circ }\cos 5^{\circ }\right)$
$=2\sin 10^{\circ }\cos 45^{\circ }-2\sin 10^{\circ }\sin 45^{\circ }$
$=0$