Home
Class 12
MATHS
Let p(k)=(1+cos((pi)/(4k)))(1+cos'((2k-1...

Let `p(k)=(1+cos((pi)/(4k)))(1+cos'((2k-1)pi)/(4k))`
`(1+cos""((2k+1)pi)/(4k))(1+cos""((4k-1)pi)/(4k))`, then

A

(a) `P(3)=1/16`

B

(b) `P(4)=(2-sqrt(2))/(16)`

C

(c) `P(5)=(3-sqrt(5))/(32)`

D

(d) `P(6)=(2-sqrt(3))/(16)`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|11 Videos
  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|13 Videos
  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS|Exercise Exercise (Single Option Correct Type Questions)|52 Videos
  • TRIGONOMETRIC EQUATIONS AND INEQUATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos
  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|9 Videos

Similar Questions

Explore conceptually related problems

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

If cosec . (pi)/(32)+ cosec. (pi)/(16)+ cosec. (pi)/(8)+ cosec. (pi)/(4)+ cosec. (pi)/(2)= cot. (pi)/(k) , then the value of k is

Prove that cos ((2pi)/7)+ cos ((4pi)/7) + cos ((6pi)/7) = - 1/2

Let S= sum_(r=1)^(5) cos (2r-1) (pi)/(11) and P=Pi_(r=1)^(4) cos (2^(r). (pi)/(15)) , then

cos^(-1)(cos""(13pi)/6)=pi/4 .

The value of : (1+cos frac (pi)(6)) (1+cos frac (pi)(3))(1+cos frac (2pi)(3)) (1+cos frac (7pi)(6)) is:

The value of overset(13)underset(k=1)(sum) (1)/(sin((pi)/(4) + ((k-1)pi)/(6)) sin ((pi)/(4)+ (kpi)/(6))) is equal to

Prove that "sin"^(2)(pi)/(6)+"cos"^(2)(pi)/(3)-"tan"^(2)(pi)/(4)=(-1)/(2)

Prove that cos^(-1)""(3)/(5)+cos^(-1)""(4)/(5)=(pi)/(2)

The value of (1+cospi/8)(1+cos(3pi)/8)(1+cos(5pi)/8)(1+cos(7pi)/8)i s (a)1/4 (b) 3/4 (c) 1/8 (d) 3/8

ARIHANT MATHS-TRIGONOMETRIC FUNCTIONS AND IDENTITIES-Exercise (More Than One Correct Option Type Questions)
  1. Let f(n)(theta)= 2 sin . (theta)/(2) sin. (3theta)/(2) + 2 sin.(theta)...

    Text Solution

    |

  2. Let P=sin 25^(@) sin 35^(@)sin 60^(@) sin 85^(@) and Q=sin20^(@)sin40...

    Text Solution

    |

  3. For 0ltphilt(pi)/(2)" if " x=sum(n=0)^(oo)cos^(2n) phi,y=sum(n=0)^(oo)...

    Text Solution

    |

  4. Let P(x)=cot^(2)x ((1+tanx+tan^(2)x)/(1+cot x+ cot^(2)x))+((cos x-cos ...

    Text Solution

    |

  5. It is known that sinbeta=4/5 and 0 < beta < pi then the value of (sqrt...

    Text Solution

    |

  6. In cyclic quadrilateral ABCD, if cot A=3/4 and tan B= (-12)/(5), then ...

    Text Solution

    |

  7. If the equation 2cos^(2)x+cosx-a=0 has solutions, then a can be

    Text Solution

    |

  8. If A=sin 44^(@)+cos44^(@), B=sin45^(@)+ cos45^(@) and C= sin46^(@)+cos...

    Text Solution

    |

  9. If tan(2alpha+beta)=x & tan(alpha+2beta)=y, then [ tan3(alpha+beta)]. ...

    Text Solution

    |

  10. If x=secphi -tanphi and y="cosec" phi+cotphi, then show that xy+x-y+1...

    Text Solution

    |

  11. If tan(x/2)=cosec x-sin x, then find the value of tan^(2) (x/2).

    Text Solution

    |

  12. If y=(sqrt(1-sin4A)+1)/(sqrt(1+sin 4A)-1), then y can be

    Text Solution

    |

  13. If 3sinbeta=sin(2alpha+beta) then

    Text Solution

    |

  14. Let P(n)(u) be a polynomial is u of degree n. Then, for every positive...

    Text Solution

    |

  15. If tan theta=(sin alpha- cos alpha)/(sin alpha+cos alpha), then:

    Text Solution

    |

  16. If cos 5 theta = a cos^(5)theta + b cos^(3)theta+c cos theta. Then, fi...

    Text Solution

    |

  17. x=sqrt(a^(2)cos^(2)alpha+b^(2)sin^(2)alpha)+sqrt(alpha^(2)sin^(2)alpha...

    Text Solution

    |

  18. Find the value of ((cosA+cosB)/(sinA-sinB))^(n)+((sinA+sinB)/(cosA-cos...

    Text Solution

    |

  19. Let p(k)=(1+cos((pi)/(4k)))(1+cos'((2k-1)pi)/(4k)) (1+cos""((2k+1)pi...

    Text Solution

    |

  20. if x = a cos^3 theta sin^2 theta and y = a cos^2 theta sin^3 theta an...

    Text Solution

    |