Home
Class 11
MATHS
Assertion (A) sum (r=1)^(n-1) cos^2((rpi...

Assertion (A) `sum _(r=1)^(n-1) cos^2((rpi)/(n))=(n)/(2)-1`
Reasion (R) : `cos alpha+ cos (alpha+ beta)+cos(alpha+2 beta)+....+cos (alpha(n-1) beta)=(sin(n beta//2))/(sin(beta//2)). Cos ((2 alpha+(n-1) beta)/(2))`

A

A is true, R is true and R is correct explanation of A

B

A is true, R is true and R is not correct explanation of A

C

A is true, R is false

D

A is false, R is true

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • REVISION EXERCISE

    AAKASH SERIES|Exercise TRANSFORMATIONS AND IDENTITIES|14 Videos

  • REVISION EXERCISE

    AAKASH SERIES|Exercise PERIOICITY, EXTREME VALUES AND GRAPHS|14 Videos

  • REVISION EXERCISE

    AAKASH SERIES|Exercise COMPOUND ANGLES|12 Videos

  • REAL FUNCTIONS

    AAKASH SERIES|Exercise EXERCISE-1|34 Videos

  • STRAIGHT LINES

    AAKASH SERIES|Exercise ADDITIONAL PRACTICE EXERCISE (LEVEL-II (ADVANCED) PRACTICE SHEET (ADDVANCED)) (Comprehension Type Questions)|6 Videos

Similar Questions

Explore conceptually related problems

If cos alpha + cos beta =0 = sin alpha + sin beta " then " cos (alpha - beta )=

2 sin^(2) beta + 4 cos( alpha+ beta) sin alpha sin beta + cos ( 2 alpha + 2 beta )=

cos^(2)(alpha+beta)+cos^(2)(alpha-beta)-cos2alpha cos2beta=

If tan(alpha-beta)=(sin 2beta)/(3-cos2beta) , then

(i) sin (alpha + beta) = sin alpha cos beta + cos alpha sin beta) (ii) sin (alpha-beta)= sin alpha cos beta- cos alpha sin beta Proof

Assertion (A) : "sin" (pi)/(n)+"sin" (3pi)/(n)+"sin"(5pi)/(n)+....+ to n terms=0 Reason (R) : sin alpha+ sin (alpha+ beta)+...+ to n terms =(Sin ((n beta)/(2)))/(Sin beta//2)xxsin ((2 alpha+(n-1)beta)/(2))

[(cos alpha-cos beta)+i(sin alpha-sinbeta)]^n+[(cos alpha-cos beta)-i(sin alpha-sin beta)]^n=

AAKASH SERIES-REVISION EXERCISE-MULTIPLE & SUB MULTIPLE ANGLES
  1. If sin 2 theta=k then the value of (tan^(3) theta)/(1+tan^(2) theta)+(...

    Text Solution

    |

  2. If sin alpha+ cos alpha= m then sin^(6)( alpha)+ cos^(6) (alpha)=

    Text Solution

    |

  3. If tan((alpha)/(2)) and tan (( beta)/(2)) are the roots of the equatio...

    Text Solution

    |

  4. "tan"^(6) (pi)/(9)-33 "tan"^(4)(pi)/(9) +27 "tan"^(2)(pi)/(9)=

    Text Solution

    |

  5. (1- sec 8 theta )/( 1- sec 4 theta ) =

    Text Solution

    |

  6. If tan ((theta)/(2))= sqrt((1-e)/(1+e)) tan(( alpha)/(2)) then cos alp...

    Text Solution

    |

  7. tan alpha+ 2 tan 2 alpha+ 4 tan4 alpha+8 cot 8 alpha=

    Text Solution

    |

  8. "cos" (2pi)/(7)+"cos" (4pi)/(7)+"cos"(6pi)/(7)=

    Text Solution

    |

  9. (1+ sec 20^(0))(1+sec40^(0))(1+ sec80^(0))=

    Text Solution

    |

  10. sin^(2)12^(0)+sin^(2)21^(0)+sin^(2)39^(0)+ sin^(2)48^(2)-sin^(2)9^(0)-...

    Text Solution

    |

  11. If cos x= tan y, cos y= tan z' cos z= tan x then

    Text Solution

    |

  12. tan20^(0)+4 sin20^(0)=

    Text Solution

    |

  13. The value of 4 sin 27^(0)=

    Text Solution

    |

  14. Statement-I : In DeltaABC, if sinA- cos B= cos C then B=(pi)/(2) Sta...

    Text Solution

    |

  15. The value of 4 sin 27^(0)=

    Text Solution

    |

  16. If A=580^(0) then -sqrt(1+sinA)-sqrt(1-sinA)=

    Text Solution

    |

  17. If cos theta- sin theta=(1)/(5), theta lt theta lt (pi)/(2) then match...

    Text Solution

    |

  18. 3 sin x+ 4 cos x= 5implies 6 tan""(x)/(2)-9 tan^(2)""(x)/(2)=

    Text Solution

    |

  19. Assertion (A) sum (r=1)^(n-1) cos^2((rpi)/(n))=(n)/(2)-1 Reasion (R)...

    Text Solution

    |

  20. Let f(k)(x)=(1)/(k)(sin^(k)x+cos^(k)x) wherex in R and k ge1, then f(4...

    Text Solution

    |