Home
Class 12
MATHS
If alpha + beta + gamma = 2 theta, prove...

If `alpha + beta + gamma = 2 theta`, prove that `cos theta + cos(theta- alpha) + cos(theta- beta) + cos(theta -gamma) = 4(cos (alpha/2) cos (beta/2) cos (gamma/2))`

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

If alpha+beta+gamma=2 theta, then cos theta+cos(theta-alpha)+cos(theta-beta)+cos(theta-gamma)

cos (alpha + beta) cos gamma-cos (beta + gamma) cos alpha = sin beta sin (gamma-alpha)

Prove that cos theta =(cos alpha- cos beta)/(1 -cos alpha*cos beta) ⇔ tan theta/2 = pm tan alpha/2 *cot beta/2 .

Prove that : cos^2 (beta-gamma) + cos^2 (gamma-alpha) + cos^2 (alpha-beta) =1+2cos (beta-gamma) cos (gamma-alpha) cos (alpha-beta) .

s(theta-alpha)=a and cos(theta-beta)=b, then sin^(2)(alpha-beta)+2ab cos(alpha-beta)=

Prove that cos alpha+cos beta+cos gamma+cos(alpha+beta+gamma)=4cos((alpha+beta)/(2))cos((beta+gamma)/(2))cos((gamma+alpha)/(2))

Prove that cos alpha+cos beta+cos gamma+cos(alpha+beta+gamma)=4cos((alpha+beta)/(2))cos((beta+gamma)/(2))cos((gamma+alpha)/(2))

It is given that cos(theta-alpha)=a, cos(theta-beta)=b What is cos(alpha-beta) equal to ?

A DAS GUPTA-Circular Functions, Identities -Exercise
  1. If A + B + C + D = 2pi, prove that: cos A + cos B + cos C + cos D =...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  11. If theta = pi/7 prove that cos theta* cos 2theta * cos 3theta = 1/8

    Text Solution

    |

  12. If alpha = (2pi)/7 prove that tan alpha *tan 2alpha + tan 2alpha* tan ...

    Text Solution

    |

  13. If alpha = 2pi/7 prove that sec alpha + sec 2alpha + sec 3alpha = -4.

    Text Solution

    |

  14. Prove that"sin"(pi)/(14)"sin"(3pi)/(14)"sin"(5pi)/(14)"sin"(7pi)/(14)=...

    Text Solution

    |

  15. Show that :sin pi/7 *sin 2pi/7* sin3pi/7 = sqrt7/8

    Text Solution

    |

  16. If u = sec theta + tan theta then tan theta in terms of u is.

    Text Solution

    |

  17. If sin x + cos x = m(ne pm 1) and sec x + cosec x = n then n in terms ...

    Text Solution

    |

  18. If alpha gt 0 such that tan(x + alpha) = tan x for all x in R then the...

    Text Solution

    |

  19. If theta = 5pi/9 the sign of the expression cos theta + sin theta is.

    Text Solution

    |

  20. If 5cos 2t + 12sin 2t = lambda sin(2t -tan^(-1)mu) where lambda, mu ar...

    Text Solution

    |