Home
Class 12
MATHS
If 2(cos ( alpha-beta)+cos(beta-gamma)+c...

If `2(cos ( alpha-beta)+cos(beta-gamma)+cos(gamma-alpha)+3=0`, prove that
`(d alpha)/(sin ( beta+theta)sin(gamma+theta))+(d beta)/(sin(alpha+beta)sin(beta+theta))+(d gamma)/(sin(alpha+theta)sin(beta+theta))=0`,
where, `'theta'` is any real angle such that `alpha+theta, beta+theta, gamma+theta` are not the multiple of `pi`.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|19 Videos

  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Single Integer Answer Type Questions)|24 Videos

  • TRIGONOMETRIC EQUATIONS AND INEQUATIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos

  • VECTOR ALGEBRA

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

Similar Questions

Explore conceptually related problems

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

Prove that: sinalpha+sinbeta+singamma-sin(alpha+beta+gamma)=4sin((alpha+beta)/2)sin((beta+gamma)/2)sin((gamma+alpha)/2)dot

Prove that: |(sinalpha, cosalpha, 1),(sinbeta, cosbeta, 1),(singamma, cosgamma, 1)|=sin(alpha-beta)+sin(beta-gamma)+sin(gamma-alpha)

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

If cos(alpha+beta)sin(gamma+delta)="cos"(alpha-beta)"sin"(gamma-delta) , prove that cotalphacotbetacotgamma=cotdelta

If x=sin(alpha-beta)*sin(gamma-delta), y=sin(beta-gamma)*sin(alpha-delta), z=sin(gamma-alpha) *sin(beta-delta) , then :

If cos(alpha+beta)*sin(gamma+delta)=cos(alpha-beta)*sin(gamma-delta), prove that cotalphacotbetacotgamma=cotdelta

If sin alpha+ sin beta+ sin gamma=3, then sin^3alpha+sin^3beta+sin^3 gamma=

If cos theta=(cos alpha cos beta)/(1-sin alpha sin beta), prove that one value of tan (theta/2)=(tan (alpha/2)-tan (beta/2))/(1-tan (alpha/2) tan (beta/2)).

If tan beta=cos theta tan alpha , then prove that tan^(2)""(theta)/(2)=(sin(alpha-beta))/(sin(alpha+beta)) .

ARIHANT MATHS ENGLISH-TRIGONOMETRIC FUNCTIONS AND IDENTITIES-Exercise (Subjective Type Questions)
  1. Prove that, cot 7 1/2 ^@ or tan 82 1/2 ^@ = (sqrt(3)+sqrt(2))(sqrt(2)+...

    Text Solution

    |

  2. If m sin (alpha+beta) = cos (alpha-beta), prove that (1)/(1- m sin 2...

    Text Solution

    |

  3. If alpha+beta+gamma=pi and tan((beta+gamma-alpha)/4)tan((gamma+alpha-b...

    Text Solution

    |

  4. The set of values of a for which the equation Sin^4 x + Cos^4 x = a ha...

    Text Solution

    |

  5. If aa n db are positive quantities such that a > b , the minimum value...

    Text Solution

    |

  6. If a, b, c and k are real constants and alpha, beta, gamma are variab...

    Text Solution

    |

  7. If (x)/(tan(theta+alpha))=(y)/(tan(theta+beta))=(z)/(tan(theta+gamma))...

    Text Solution

    |

  8. Let f(x)=cos(a1+x)+1/2cos(a2+x)+1/(2^2)cos(a1+x)++1/(2^(n-1))cos(an+x)...

    Text Solution

    |

  9. Eliminate theta from the equations tan(n theta+alpha)-tan(n theta+b...

    Text Solution

    |

  10. If A, B, C are the angle of a triangle and |(sinA,sinB,sinC),(cosA,...

    Text Solution

    |

  11. In any DeltaABC, prove that Sigma (sqrt(sinA))/(sqrt(sinB)+sqrt(sinC...

    Text Solution

    |

  12. If 2(cos ( alpha-beta)+cos(beta-gamma)+cos(gamma-alpha)+3=0, prove tha...

    Text Solution

    |

  13. If the quadratic equation , 4^(sec^(2)alpha) x^(2) + 2x + (beta^(2)-...

    Text Solution

    |

  14. If (cos theta(1))/(cos theta(2))+(sin theta(1))/(sin theta(2))=(cos th...

    Text Solution

    |

  15. Prove that sum(k=1)^(n-1) ""^(n)C(k)[cos k x. cos (n+k)x+sin(n-k)x.s...

    Text Solution

    |

  16. Total number of solution for the equation x^(2)-3[sin(x-(pi)/6)]=3 is ...

    Text Solution

    |

  17. In aDeltaABC, prove that Sigma(r=0)^(n)""^(n)C(r)a^(r)b^(n-r) cos ( ...

    Text Solution

    |

  18. Resolve Z^5+ 1 into linear & quadratic factors with real coefficients...

    Text Solution

    |

  19. Prove that the roots of the equation 8x^(3)-4x^(2)-4x+1=0 " are " co...

    Text Solution

    |