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AP EAMCET · Maths · Trigonometric Ratios & Identities

\(\cos 66^{\circ}+\sin 84^{\circ}=\)

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

Answer & Solution

Correct Answer

(D) \(\frac{1}{4} \sqrt{3}(\sqrt{5}+1)\)

Step-by-step Solution

Detailed explanation

\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}…