Home
Class 12
MATHS
Sum the series: sin alpha - sin 2alpha ...

Sum the series: `sin alpha - sin 2alpha + sin 3alpha - sin 4alpha` + ... to n terms.

Text Solution

AI Generated Solution

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

(sqrt2 - sin alpha - cos alpha )/( sin alpha - cos alpha)=

If sin 3 alpha =4 sin alpha sin (x+alpha ) sin(x-alpha ) , then

sin3 alpha=4sin alpha sin(x+alpha)sin(x-alpha)

Find the sum of the infinite series, sinalpha+1/2 sin2alpha+1/2^2sin3alpha+1/2^3sin4alpha+.......oo.

Sum: sqrt(1 + sin 2alpha) + sqrt(1 + sin 4alpha) + sqrt(1 + sin 6alpha) +... to 20 terms.

If alpha=(pi)/(17), then the value of (sin21 alpha-sin alpha)/(sin16 alpha+sin4 alpha) is equal to

Sum of n terms of the series sinalpha-sin(alpha+beta)+sin(alpha+2beta)-sin(alpha+3beta)+….

sin alpha * sin (60-alpha) sin (60 + alpha) = (1) / (4) * sin3 alpha

sin alpha-cos alpha=(1)/(3) then sin^(4)alpha-cos^(4)alpha=

A DAS GUPTA-Circular Functions, Identities -Exercise
  1. Prove that cosec 2alpha = cot alpha - cot 2alpha. Hence or otherwise ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  19. If x + y + z = xyz, prove that (3x -x^(3))/ (1-3x^(2)) + (3y -y^(3))/(...

    Text Solution

    |

  20. If A + B + C = pi then show that cot theta = cot A + cot B + cot C ⇔ s...

    Text Solution

    |