AP EAMCET · Maths · Trigonometric Ratios & Identities
If \(\cos A+\cos (A+B)+\cos (A+2 B)+\ldots\) upto \(n\) terms \(=\) \(\cos \left(\frac{2 \mathrm{~A}+(\mathrm{n}-1) \mathrm{B}}{2}\right) \sin \frac{\mathrm{nB}}{2} \operatorname{cosec} \frac{\mathrm{B}}{2}\),
then \(\cos \frac{\pi}{19}+\cos \frac{3 \pi}{19}+\cos \frac{5 \pi}{19}+\ldots+\cos \frac{17 \pi}{19}=\)
- A 1
- B \(-\frac{1}{2}\)
- C \(\frac{1}{2}\)
- D 0
Answer & Solution
Correct Answer
(C) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
Given, \(\cos A+\cos (A+B)+\cos (A+2 B)+\ldots\) upto \(n\) terms \(=\cos \left(\frac{2 A+(n-1) B}{2}\right) \sin \frac{n B}{2} \operatorname{cosec} \frac{B}{2}\) Now, \(\cos \frac{\pi}{19}+\cos \frac{3 \pi}{19}+\cos \left(\frac{5 \pi}{19}\right)+\ldots+\cos \frac{17 \pi}{19}\)…
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