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TS EAMCET · Maths · Trigonometric Ratios & Identities

\[ \sin 6^{\circ}+\sin 54^{\circ}+\sin 126^{\circ}+\cos 156^{\circ}= \]

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

Answer & Solution

Correct Answer

(A) \(\frac{\sqrt{5}+1}{4}\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text { } \sin 6^{\circ}+\sin 54^{\circ}+\sin 126^{\circ}+\cos 156^{\circ} \\ & =\sin 6^{\circ}+\cos \left(90^{\circ}+66^{\circ}\right)+\sin 54^{\circ}+\sin \left(90^{\circ}+36^{\circ}\right) \\ & =\sin 6^{\circ}-\sin 66^{\circ}+\sin 54^{\circ}+\cos 36^{\circ}…