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AP EAMCET · Maths · Trigonometric Ratios & Identities

If \(A=\frac{\pi}{24}\), then \(\frac{\cos A+\cos 3 A+\cos 5 A+\cos 7 A}{\sin A+\sin 3 A+\sin 5 A+\sin 7 A}=\)

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

Answer & Solution

Correct Answer

(A) \(\sqrt{3}\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text {Let } I=\frac{\cos A+\cos 3 A+\cos 5 A+\cos 7 A}{\sin A+\sin 3 A+\sin 5 A+\sin 7 A} \\ & \Rightarrow I=\frac{(\cos A+\cos 7 A)+(\cos 5 A+\cos 3 A)}{(\sin A+\sin 7 A)+(\sin 5 A+\sin 3 A)} \\ & \Rightarrow I=\frac{\cos 4 A[2 \cos 3 A+2 \cos A]}{\sin 4 A[2…