\(\cos 48^{\circ} \cdot \cos 12^{\circ}=\)
\(\cos 48^{\circ} \cdot \cos 12^{\circ}=\)
- \(\frac{(3-\sqrt{5)}}{8}\)
- \(\frac{(3+\sqrt{5})}{4}\)
- \(\frac{(3+\sqrt{5})}{2}\)
- \(\frac{(3+\sqrt{5})}{8}\)
Solution
\(\begin{aligned}
& \cos 48^{\circ} \cdot \cos 12^{\circ}=\frac{1}{2}\left(2 \cos 48^{\circ} \cdot \cos 12^{\circ}\right) \\
&=\frac{1}{2}\left[\cos 60^{\circ}+\cos 36^{\circ}\right]=\frac{1}{2}\left[\frac{1}{2}+\frac{\sqrt{5}+1}{4}\right] \\
&=\left(\frac{3+\sqrt{5}}{8}\right)
\end{aligned}\)
Asked in: AP EAMCET 2020 (17 Sep Shift 1)
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