Home
Class 12
MATHS
Prove that cosec 2alpha = cot alpha - co...

Prove that `cosec 2alpha = cot alpha - cot 2alpha`. Hence or otherwise prove that `cosec theta + cosec 2theta + cosec 4theta + cosec 8theta = cot theta/2 - cot 8theta`.

Promotional Banner

Topper's Solved these Questions

  • Circular Functions, Identities

    A DAS GUPTA|Exercise Exercise|300 Videos

  • Circles

    A DAS GUPTA|Exercise EXERCISE|122 Videos

  • COMPLEX NUMBERS

    A DAS GUPTA|Exercise EXERCISE|224 Videos

Similar Questions

Explore conceptually related problems

If cosec theta + cot theta= p , cos theta = ?

Prove that: cot theta + tan theta = cosec theta sec theta .

Prove that ( cot theta - cosec theta)^(2) = ( 1- cos theta )/( 1+ cos theta )

Prove that cot^4 theta+ cot^2 theta= cosec^4 theta-cosec^2 theta

Prove that (cot theta + "cosec" theta -1 )/(cot theta - "cosec" theta +1)=(1+ cos theta)/(sin theta).

Find cos theta, if 6 cot theta+2 "cosec" theta= cot theta+5 "cosec" theta .

If cosec theta + cot theta= 2.5 , then cosec theta = ?

Prove that : (sin theta)/(1 - costheta) = cosec theta + cot theta

Prove that (cot^(2)theta)/(cosec theta+1)=cosec theta-1

A DAS GUPTA-Circular Functions, Identities -Exercise
  1. Prove that tan alpha + 2tan 2alpha + 4tan 4alpha + 8cot 8alpha = cot ...

    Text Solution

    |

  2. Find the sum: tan x + 1/2 tan x/2+ 1/2^(2) tan x/2^(2) +.....+1/2^(n-...

    Text Solution

    |

  3. Prove that cosec 2alpha = cot alpha - cot 2alpha. Hence or otherwise ...

    Text Solution

    |

  4. Prove that sum(r=1)^(10) = sin^(2) rpi/18 =5.

    Text Solution

    |

  5. Sum the series: sin alpha - sin 2alpha + sin 3alpha - sin 4alpha + .....

    Text Solution

    |

  6. Find sum(r=1)^(10) cos^(3) rpi/3.

    Text Solution

    |

  7. Sum: sqrt(1 + sin 2alpha) + sqrt(1 + sin 4alpha) + sqrt(1 + sin 6alpha...

    Text Solution

    |

  8. Prove that sin^(2) 12^circ + sin^(2)21^circ + sin^(2)39^circ + sin^(2)...

    Text Solution

    |

  9. If A + B + C = pi, prove that cos A cosec B cosec C + cos B cosec C c...

    Text Solution

    |

  10. Prove that in a triangle ABC, sin^(2)A - sin^(2)B + sin^(2)C = 2sin A...

    Text Solution

    |

  11. Prove that in a triangle ABC, sum (cot B+ cotC)/(tan B + tan C) =1.

    Text Solution

    |

  12. If A +B+C = 180^circ, prove that cos A/2+ cos B/2 +cos C/2 = 4cos (p...

    Text Solution

    |

  13. If alpha + beta- gamma= pi, prove that sin^(2)alpha + sin^(2)beta - s...

    Text Solution

    |

  14. If alpha + beta + gamma = 2 theta, prove that cos theta + cos(theta- ...

    Text Solution

    |

  15. If A + B + C = pi, show that cot A + sinA/(sin B sin C) = cot B + sin...

    Text Solution

    |

  16. If A + B + C = 0, prove that sum sin 2A = 2sum sin A * (1 + sum cos A...

    Text Solution

    |

  17. Prove that tan(x - y) + tan(y - z) + tan(z - x) = tan(x - y) *tan(y -...

    Text Solution

    |

  18. If alpha + beta + gamma + delta = 2pi then prove that sum tan alpha =...

    Text Solution

    |

  19. If cos(beta - gamma) * cos(gamma - alpha)* cos(alpha - beta) + 1 = 0 ...

    Text Solution

    |

  20. If x + y + z = xyz, prove that x(1 -y^(2)) (1- z^(2))+ y(1- z^(2))(1- ...

    Text Solution

    |