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AP EAMCET · Maths · Trigonometric Ratios & Identities

\(\cos 48^{\circ} \cdot \cos 12^{\circ}=\)

  1. A \(\frac{(3-\sqrt{5)}}{8}\)
  2. B \(\frac{(3+\sqrt{5})}{4}\)
  3. C \(\frac{(3+\sqrt{5})}{2}\)
  4. D \(\frac{(3+\sqrt{5})}{8}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{(3+\sqrt{5})}{8}\)

Step-by-step Solution

Detailed explanation

\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)…