JEE Mains · Maths · STD 11 - 3. trignometrical ratios,functions and identities
If \(A = \dfrac{\sin 3^\circ}{\cos 9^\circ} + \dfrac{\sin 9^\circ}{\cos 27^\circ} + \dfrac{\sin 27^\circ}{\cos 81^\circ}\) and \(B = \tan 81^\circ - \tan 3^\circ\), then \(\dfrac{B}{A}\) is equal to _____.
- A 1
- B 2
- C 3
- D 4
Answer & Solution
Correct Answer
(B) 2
Step-by-step Solution
Detailed explanation
Consider the general term \(\dfrac{\sin x}{\cos 3x}\). We can rewrite this by multiplying and dividing by \(2\cos x\): \(\dfrac{2\sin x \cos x}{2\cos 3x \cos x} = \dfrac{\sin 2x}{2\cos 3x \cos x}\) Using \(\sin 2x = \sin(3x - x) = \sin 3x \cos x - \cos 3x \sin x\), we get:…
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