Home
Class 12
MATHS
The value of cos""(pi)/(11)+cos""(3pi)/(...

The value of `cos""(pi)/(11)+cos""(3pi)/(11)+cos""(5pi)/(11)+cos""(7pi)/(11)+cos""(9pi)/(11),` is

Text Solution

Verified by Experts

The correct Answer is:
`1//2`
We have
`cos""(pi)/(11)+cos""(3pi)/(11)+cos""(5pi)/(11)+cos""(7pi)/(11)+cos""(9pi)/(11)`
`=(cos((5pi)/(11)).sin((pi)/(11)+(9pi)/(1))/(2))/(sin((pi)/(11)))`
`=(cos""(5pi)/(11)sin""(5pi)/(11))/(sin""(pi)/(11))=(1)/(2)((10pi)/(11))/(sin((pi)/(1)))=(1)/(2)`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise 3.8|9 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise 3.9|5 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise 3.6|5 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

  • TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Multiple Correct Answers Type|6 Videos

Similar Questions

Explore conceptually related problems

cos""(2pi)/(15)cos""(4pi)/(15)cos""(8pi)/(15)cos""(16pi)/(15)=(1)/(16)

Prove that 2 cos""(pi)/(13)cos""(9pi)/(13)+cos""(3pi)/(13)+cos""(5pi)/(13)=0

Show that cos (pi)/(15) cos""(2pi)/(15) cos"" (3pi)/(15) cos"" (4pi)/(15) cos"" (5pi)/(15) cos"" (6pi)/(15) cos"" (7pi)/(15) = (1)/(128) .

Find the value of cos^2pi/(16)+cos^2(3pi)/(16)+cos^2(5pi)/(16)+cos^2(7pi)/(16)dot

Find the value of cos^(-1)(cos""(pi)/(7)cos""(pi)/(17)-sin""(pi)/(7)sin""(pi)/(17))

(1 + cos"" (pi)/(8))(1 + cos"" (3pi)/(8)) (1 + cos"" (5pi)/(8))(1 + cos"" (7pi)/(8)) =

Prove that 32 (sqrt(3)) sin"" (pi)/(48) cos"" (pi)/(48) cos"" (pi)/(24) cos"" (pi)/(12) cos"" (pi)/(6) = 3