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  4. The value of the expression, cos 35°+ cos 125°+ 2 sin 185°( sin 130°+ sin 140°) is

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

Trigonometric Functions

Solution:

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