Question

$\cos 66^{\circ }+\sin 84^{\circ }=$

• A. $\frac{1}{4}(\sqrt{3}+\sqrt{5})$
• B. $\frac{1}{4}\sqrt{5}(\sqrt{3}+1)$
• C. $\frac{1}{4}(\sqrt{3}+1)(\sqrt{5}+1)$
• D. $\frac{1}{4}\sqrt{3}(\sqrt{5}+1)$

Answer 1

Answer: (D)

$\cos 66^{\circ }+\sin 84^{\circ }=\cos 66^{\circ }+\cos 6^{\circ }$
$=2\cos 36^{\circ }\cos 30^{\circ }$
$\left[\because \cos C+\cos D=2\cos \frac{C+D}{2}\cos \frac{C-D}{2}\right]$
$=\sqrt{3}\cos 36^{\circ }=\sqrt{3}\frac{(\sqrt{5}+1)}{4}\left[\because \cos 36^{\circ }=\frac{\sqrt{5}+1}{4}\right]$