Home
Class 14
MATHS
If sin alpha + sin beta = a " and " cos ...

If `sin alpha + sin beta = a " and " cos alpha + cos beta = b` then proved that `cos(alpha - beta) = (a^(2) + b^(2) - 2)/(2) " and " tan ""(alpha - beta)/(2) = pm sqrt (4-a^(2)-b^(2))/(a^(2)+b^(2))`.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • ADVANCED TRIGONOMETRIC IDENTITIES

    LUCENT PUBLICATION|Exercise EXERCISE 13A|49 Videos

  • ALGEBRAIC IDENTITIES

    LUCENT PUBLICATION|Exercise Exercise - 1B|28 Videos

Similar Questions

Explore conceptually related problems

If sin alpha+sin beta=a and cos alpha+cos beta=b prove that :cos(alpha-beta)=(1)/(2)(a^(2)+b^(2)-2)

If s in alpha+s in beta=a and cos alpha+cos beta=b prove that: cos(alpha-beta=(a^(2)+b^(2)-2)/(2))

If sin alpha+sin beta=a and cos alpha-cos beta=b then tan((alpha-beta)/(2))=

If sin alpha+sin beta=a and cos alpha+cos beta=b prove that tan((alpha-beta)/(2))=+-sqrt((4-a^(2)-b^(2))/(a^(2)+b^(2)))

If s in alpha+s in beta=a and cos alpha+cos beta=b show that :sin( alpha + beta )=(2a)/(a^(2)+b^(2))

If s in alpha+s in beta=a and cos alpha+cos beta=b show that :cos(alpha+beta)=(b^(2)-a^(2))/(b^(2)+a^(2))

If sin alpha+sin beta=a and cos alpha+cos beta=b then tan((alpha-beta)/(2)) is equal to

If sin alpha+sin beta=a and cos alpha+cos beta=b show that sin(alpha+beta)=(2ab)/(alpha^(2)+beta^(2))

If s in alpha+s in beta=a and cos alpha-cos beta=b then (tan(alpha-beta))/(2)=-(a)/(b) b.(b)/(a) c.sqrt(a^(2)+b^(2)) d.none of these

LUCENT PUBLICATION-ADVANCED TRIGONOMETRIC IDENTITIES-EXERCISE 13A
  1. If sin alpha + sin beta = a " and " cos alpha + cos beta = b then prov...

    Text Solution

    |

  2. If p and q are two quantities such that p^(2) +q^(2) =1, then maximum...

    Text Solution

    |

  3. If theta is real then 3 - cos theta + cos (theta + (pi)/(3)) lies in t...

    Text Solution

    |

  4. If sinA=(1)/(sqrt(10))andsinB=(1)/(sqrt(5)), where A and B are positiv...

    Text Solution

    |

  5. If cos (theta - alpha) = a, cos (theta - beta) = b, then the value of ...

    Text Solution

    |

  6. A positive acute angle is divided into two parts whose tangents are 1/...

    Text Solution

    |

  7. In trianglePQR, angleR = (pi)/(2). If tan((P)/(2)) " and " tan ((Q)/...

    Text Solution

    |

  8. The value of (sin 55^(@) - cos 55^(@))/(sin10^(@) is

    Text Solution

    |

  9. The value of cos 15^(@) - sin 15^(@) is

    Text Solution

    |

  10. Minimum value of 27^(cos 2x) 81^( sin 2x) is

    Text Solution

    |

  11. 3 (sinx - cosx)^(4) + 6 (sinx + cosx)^(2) + 4(sin^(6)x + cos^(6)x) =

    Text Solution

    |

  12. If sin theta = sin 15^(@) + sin 45^(@), " where " 0^(@) lt theta lt ...

    Text Solution

    |

  13. If cos alpha + cos beta = 0 = sin alpha + sin beta, then value of cos...

    Text Solution

    |

  14. If A + B = 45^(@), " then " (cot A - 1) ( cot B - 1) is

    Text Solution

    |

  15. If alpha, beta in (0, (pi)/(2)), sin alpha = (4)/(5) " and " cos (alp...

    Text Solution

    |

  16. The value of tan 40^(@) + tan 20^(@) + sqrt(3) tan 20^(@) tan 40^(@) ...

    Text Solution

    |

  17. The value of cos 20^(@) + Cos 100^(@) + cos 140^(@) is

    Text Solution

    |

  18. If (-pi)/(2) < theta < (pi)/(2) " and " theta ne pm (pi)/(4), then th...

    Text Solution

    |

  19. If sin theta =3 sin ( theta + 2 alpha), then the value of tan (theta...

    Text Solution

    |

  20. If x=ycos""(2pi)/(3)=zcos""(4pi)/(3), then xy+yz+zx is equal to

    Text Solution

    |

  21. (cos 9^(@) + sin 9^(@))/(cos 9^(@) - sin 9^(@)) equals

    Text Solution

    |