Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • The value of <img alt="cos\ \frac{\pi}{11}+cos\ \frac{3\pi}{11}+cos\ \frac{5\pi}{11}+cos\ \frac{7\pi}{11}+cos\ \frac{9\pi}{11}" src="https://entrancecorner.oncodecogs.com/gif.latex?c

The value of cos\ \frac{\pi}{11}+cos\ \frac{3\pi}{11}+cos\ \frac{5\pi}{11}+cos\ \frac{7\pi}{11}+cos\ \frac{9\pi}{11} is

 

Option: 1

1


Option: 2

-1


Option: 3

\frac{1}{2}


Option: 4

-\frac{1}{2}


Answers (1)

best_answer

Answer: Option (c)   \frac{1}{2}

Explanation: 

Given that,

cos\ \frac{\pi}{11}+cos\ \frac{3\pi}{11}+cos\ \frac{5\pi}{11}+cos\ \frac{7\pi}{11}+cos\ \frac{9\pi}{11}Here,

Difference   d=\frac{2\pi}{11}

n=5

cos\ \frac{\pi}{11}+cos\ \frac{3\pi}{11}+cos\ \frac{5\pi}{11}+cos\ \frac{7\pi}{11}+cos\ \frac{9\pi}{11}=\frac{sin\left ( \frac{5\times \frac{2\pi}{11}}{2}\right )\cdot cos\left (\frac{\frac{\pi}{11}+\frac{9\pi}{11}}{2}\right )}{sin\left ( \frac{2\pi}{11\times 2} \right )}

cos\ \frac{\pi}{11}+cos\ \frac{3\pi}{11}+cos\ \frac{5\pi}{11}+cos\ \frac{7\pi}{11}+cos\ \frac{9\pi}{11}=\frac{2sin\left ( \frac{5\pi}{11} \right )cos\left ( \frac{5\pi}{11} \right )}{2sin\left ( \frac{\pi}{11} \right )}

 cos\ \frac{\pi}{11}+cos\ \frac{3\pi}{11}+cos\ \frac{5\pi}{11}+cos\ \frac{7\pi}{11}+cos\ \frac{9\pi}{11}=\frac{sin\frac{10\pi}{11}}{2sin\frac{\pi}{11}}

cos\ \frac{\pi}{11}+cos\ \frac{3\pi}{11}+cos\ \frac{5\pi}{11}+cos\ \frac{7\pi}{11}+cos\ \frac{9\pi}{11}=\frac{sin\left ( \pi-\frac{\pi}{11} \right )}{2sin\frac{\pi}{11}}

cos\ \frac{\pi}{11}+cos\ \frac{3\pi}{11}+cos\ \frac{5\pi}{11}+cos\ \frac{7\pi}{11}+cos\ \frac{9\pi}{11}=\frac{1}{2}

Posted by

HARSH KANKARIA

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Latest Question