Home
Class 12
MATHS
Let f(n)(theta)= 2 sin . (theta)/(2) sin...

Let `f_(n)(theta)= 2 sin . (theta)/(2) sin. (3theta)/(2) + 2 sin.(theta)/(2) sin. (5theta)/(2) + 2sin. (theta)/(2) sin. (7 theta)/(2) + ... + 2 sin (2 n+1) (theta)/(2), n in N`,
then which of the following is/are correct ?

A

`f_(9)(pi/4)=(1)/(sqrt(2))`

B

`f_(n)((2pi)/(n))=0, n in N`

C

`f_(3)((2pi)/(7))=0`

D

`f_(9)(pi/4)=-(1)/(sqrt(2))`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
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

Prove that : cos2 theta cos frac (theta)(2)- cos3 theta cos frac (9 theta)(2)= sin 5 theta sin frac (5theta)(2).

Prove that : (sin theta)/(1+cos theta) + (1+cos theta)/(sin theta)= 2 cosec theta .

Prove that : sin 2 theta= 2sin theta cos theta .

Prove that (1+sin2theta)/(1-sin2theta)=((1+tantheta)/(1-tan theta))^(2)

Let A = [ (cos theta, sin theta),(- sin theta, cos theta)] , then show that A ^(2) = [(cos 2 theta, sin 2 theta),( - sin 2 theta, cos 2 theta)]

Find theta such that (3+2i sin theta)/(1-2i sin theta) is purely real.

Express sin^(5)theta in term of sin ( n theta), n in N .

Prove that ((1+sintheta)^2+(1-sintheta)^2)/(2cos^2theta)=(1+sin^2theta)/(1-sin^2theta) .

Prove the following identity : (sin theta)/(1+cos theta)+ (sin theta)/(1-cos theta)= 2/(sin theta) .

Prove that : sin^8 theta- cos^8 theta= (sin^2 theta- cos^2 theta)(1-2 sin^2 theta cos^2 theta) .

ARIHANT MATHS-TRIGONOMETRIC FUNCTIONS AND IDENTITIES-Exercise (More Than One Correct Option Type Questions)
  1. Suppose cos x = 0 and cos(x+z)=1/2. Then, the possible value (s) of z ...

    Text Solution

    |

  2. Let f(n)(theta)= 2 sin . (theta)/(2) sin. (3theta)/(2) + 2 sin.(theta)...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |