$\cos 66^{\circ}+\sin 84^{\circ}=$
$\cos 66^{\circ}+\sin 84^{\circ}=$
- $\frac{1}{4}(\sqrt{3}+\sqrt{5})$
- $\frac{1}{4} \sqrt{5}(\sqrt{3}+1)$
- $\frac{1}{4}(\sqrt{3}+1)(\sqrt{5}+1)$
- $\frac{1}{4} \sqrt{3}(\sqrt{5}+1)$
Solution
$
\begin{aligned}
& \cos 66^{\circ}+\sin 84^{\circ}=\cos 66^{\circ}+\cos 6^{\circ} \\
& =2 \cos 36^{\circ} \cos 30^{\circ} \\
& \quad\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} \quad\left[\because \cos 36^{\circ}=\frac{\sqrt{5}+1}{4}\right]
\end{aligned}
$
Hence, option (d) is correct
Asked in: AP EAMCET 2019 (20 Apr Shift 2)
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