Home
Class 12
MATHS
Eliminate theta between a = cos(theta - ...

Eliminate `theta` between `a = cos(theta - alpha)`, `b = sin(theta - beta)` and prove that `a^(2) -2ab sin(alpha - beta) + b^(2) = cos^(2)(alpha - beta)`.

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 cos(theta-alpha)=a,sin(theta-beta)=b, prove that a^(2)-2ab sin(alpha-beta)+b^(2)=cos^(2)(alpha-beta)

If cos (theta - alpha) = a, cos (theta - beta) = b , then the value of sin^(2) (alpha - beta) + 2ab cos (alpha - beta) is

If cos (theta -alpha) =a, sin (theta - beta) =b, then cos ^(2) (alpha - beta) + 2 ab sin (alpha - beta) is equal to

If sin(theta+alpha)=a and sin(theta+beta)=b, prove that cos2(alpha-beta)-4ab cos(alpha-beta)=1-2a^(2)-2b^(2)

If cos(theta-alpha)=p and sin(theta+beta)=q show that p^(2)+q^(2)-2pq sin(alpha+beta)=cos^(2)(alpha+beta)

If cos (theta - alpha) = a and sin(theta - beta) = b (0 lt theta - alpha, theta - beta lt pi//2) , then prove that cos^(2) (alpha - beta) + 2ab sin (alpha - beta) = a^(2) + b^(2)

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

If cos(theta-alpha)=a and cos(theta-beta)=b then the value of sin^(2)(alpha-beta)+2ab cos(alpha-beta)

sin(theta+alpha)=a sin(theta+beta)=b(0

A DAS GUPTA-Circular Functions, Identities -Exercise
  1. If cos alpha + cos 2alpha = p,sin alpha + sin 2alpha = q then eliminat...

    Text Solution

    |

  2. If cos alpha = cos beta*cos phi= cos gamma *cos theta and sin alpha = ...

    Text Solution

    |

  3. Eliminate theta between a = cos(theta - alpha), b = sin(theta - beta) ...

    Text Solution

    |

  4. Eliminating alpha from xcos alpha = y cos(alpha +2pi/3) = zcos (alpha ...

    Text Solution

    |

  5. If cos rx + cos ry = ar, r = 1, 2, 3 then prove that 2a1^(3) + a3 = 3...

    Text Solution

    |

  6. Eliminate theta, phi from sin theta + sin phi = a, cos theta+ cos phi ...

    Text Solution

    |

  7. Eliminatetheta from lambda cos 2theta = cos(theta + alpha) and lambda...

    Text Solution

    |

  8. If f(theta) = 1 + sin [pi/4 + theta] + cos (pi/4 + theta). find the ra...

    Text Solution

    |

  9. Prove that the value of 5 cos theta + 3cos (theta + pi/3) +3 lies bet...

    Text Solution

    |

  10. If f(theta) = 11cos^(2)theta + 15sin theta cos theta - 9sin^(2)theta, ...

    Text Solution

    |

  11. Find the maximum and minimum values of sin^(6)x + cos^(6)x.

    Text Solution

    |

  12. In triangle ABC, B = pi/3 and sin A . sin C = x then find the set of ...

    Text Solution

    |

  13. Prove that the relation sin^(2)theta = (x+y)^(2)/(4xy) is not possib...

    Text Solution

    |

  14. Prove that sin theta = x + p/x is possible for real x if p le 1/4

    Text Solution

    |

  15. If f(x) = 3(sin x - cos x)^(4) + 6(sin x + cos x)^(2) +4(sin^(6)x + co...

    Text Solution

    |

  16. If alpha, beta are acute angles and cos 2alpha = (3cos2beta -1)/(3-cos...

    Text Solution

    |

  17. If tan theta* tan phi = sqrt((x-y)/(x+y)) prove that (x - y cos 2the...

    Text Solution

    |

  18. If x in (pi, 2pi), prove that ((sqrt(1+cosx))+(sqrt(1-cos x)))/((sqrt(...

    Text Solution

    |

  19. Show that cot theta* cot 2theta+ cot 2theta *cot 3theta + 2 = cot thet...

    Text Solution

    |

  20. If tan^(3) (alpha/2+ pi/4) = tan(beta/2 +pi/4) then prove that sin be...

    Text Solution

    |