Question 54

Simplify: $$cos 18^\circ + cos 162^\circ + sin 126^\circ + sin 234^\circ$$

Solution

$$\cos18^{\circ\ }=\cos\left(180^{\circ\ }-162^{\circ\ }\right)=-\cos162^{\circ\ }.$$

$$\sin126^{\circ\ }=\sin\left(360^{\circ\ }-234^{\circ\ }\right)=-\sin234^{\circ\ }.$$

So,

$$\cos18^{\circ}+\cos162^{\circ}+\sin126^{\circ}+\sin234^{\circ}$$

$$=-\cos162^{\circ}+\cos162^{\circ}-\sin234^{\circ}+\sin234^{\circ}.$$

$$=0.$$

D is correct choice.

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