Home
Class 12
MATHS
underset(r=0)overset(n)(sum)sin^(2)""(rp...

`underset(r=0)overset(n)(sum)sin^(2)""(rpi)/(n)` is equal to

Text Solution

Verified by Experts

The correct Answer is:
`n//2`
`sum_(r=1)^(n-1)sin^(2)""(rpi)/(n)=sum_(r=1)^(n-1)(1-cos(2rpi//n))/(2)`
`=(1)/(2)(n-1-(sin(n-1)(pi)/(n))/(sin((pi)/(n)))cos(((2pi)/(n)+(n-1)(2pi)/(n))/(2)))`
`=(1)/(2)(n-1-(sin((pi)/(n)))/(sin((pi)/(n)))(-1))=(n)/(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

sum_(r=0)^(n) sin^(2)""(rpi)/(n) is equal to

If k=underset(r=0)overset(n)(sum)(1)/(.^(n)C_(r)) , then underset(r=0)overset(n)(sum)(r)/(.^(n)C_(r)) is equal to

sum_(r=1)^(n-1)cos^(2)""(rpi)/(n) is equal to

underset(r=1)overset(n)sum ( r )/(r^(4)+r^(2)+1) is equal to

let underset(r=0)overset(2010)(sum)a_(r)x^(r)=(1+x+x^(2)+x^(3)+x^(4)+x^(5))^(402) and underset(r=0)overset(2010)(sum)a_(r)=a, then the value of ((underset(r=0)overset(2010)(sum)r.a_(r))/(underset(r=0)overset(2010)(sum)a_(r))) is equal to____.

underset(r=1)overset(n)(sum)r(.^(n)C_(r)-.^(n)C_(r-1)) is equal to