Home
Class 12
MATHS
Prove that in a triangle ABC, sin^(2)A ...

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

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

Prove that in triangle ABC,cos^(2)A+cos^(2)B-cos^(2)C=1-2sin A sin B cos C

"In triangle ABC " "c(sin^(2)A+sin^(2)B)=sin C(a sin A+b sin B)

In any triangle ABC,sin^(2)A-sin^(2)B+sin^(2)C is always equal to (A) 2sin A sin B cos C(B)2sin A cos B sin C(C)2sin A cos B cos C(D)2sin A sin B sin C

If A+B+C= 180^(@) , prove that: (i) "sin"^(2)+"sin"^(2)B-"sin"^(2)C=2 "sin"A sin B cos C (ii) "sin"^(2)A-"sin"^(2)B+"sin"^(2) C=2 sin Acos B sin C.

In triangle ABC, prove that sin(B+C-A)+sin(C+A-B)+sin(A+B-C)=4sin A sin B sin C .

If : A+B+C=pi, "then"" "sin ^(2) A +sin^(2)B - sin ^(2)C= A) 2 cos A * cos B * sin C B) 2 cos B * cos C * sin A C) 2 sin A * sin B * cos C D) 2 sin B * sin C * cos A

If in a triangle ABC, |{:(1, sin A ,sin^(2)A),(1,sin B , sin^(2)B),(1, sin C, sin^(2)C):}|= 0 then the triangle is

In any triangle ABC,prove that sin^(3)A cos(B-C)+sin^(3)B cos(C-A)+sin^(3)C cos(A-B)=3sin A sin B sin C

A DAS GUPTA-Circular Functions, Identities -Exercise
  1. Prove that sin^(2) 12^circ + sin^(2)21^circ + sin^(2)39^circ + sin^(2)...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  17. If alpha = 2pi/7 prove that tan alpha *tan 2alpha + tan 2alpha* tan 4a...

    Text Solution

    |

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

    Text Solution

    |

  19. Prove that sin pi/14* sin 3pi/14 * sin 5pi/14 = 1/8.

    Text Solution

    |

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

    Text Solution

    |