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)

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