AP EAMCET · Maths · Trigonometric Ratios & Identities
\(\cos 66^{\circ}+\sin 84^{\circ}=\)
- 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 & 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}…
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