Home
Class 11
MATHS
Prove that in a A B C ,sin^2A+sin^2B+si...

Prove that in a ` A B C ,sin^2A+sin^2B+sin^2C<=9/4dot`

Text Solution

Verified by Experts

`cos2A=1-2sin^2A`
`sin^2A=(1-cos2A)/2`
`=(1-cos2A)/2+(1-cos2B)/2+sin^2C`
`=1+sin^2C-1/2(cos2A+cos2B)`
`=1+sin^2C-1/2(2cos(A_B)*cos(A-B))`
`=1+sin^2C-cos(A+B)*cos(A-B)`
`A+B+C=pi`
`A+B=pi-C`
...
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE ENGLISH|Exercise All Questions|491 Videos

Similar Questions

Explore conceptually related problems

If A+B+C = pi , prove that : sin^(2)A +sin^(2)B +sin^(2)C = 2(1+cosAcosBcosC)

If A+B+C=180^0 , prove that : sin^2 A + sin^2 B + sin^2 C =2 (1+cosA cosB cosC)

If A+B+C = 180^0 , Prove that : sin^2 (A/2) + sin^2 (B/2) + sin^2 (C/2) =1-2 sin (A/2) sin (B/2) sin (C/2)

If A + B + C = 180^@ , then prove that sin 2 A+ sin 2B + sin 2C = 4 sin A sin B sin C

If A+B+C=pi , prove that : sin2A+sin2B+sin2C=4sinA sinB sinC

Prove that sin2A + sin2B + sin2C = 4sinA · sinB · sin C

If A+B+C=pi and A+B=2C , prove that : 4 (sin^2 A + sin^2 B - sinA sinB)=3 .

In DeltaABC , prove that: a) (sin2A + sin2B + sin2C)/(sinA+sinB+sinC) = 8sin(A/2) sin(B/2)sin(C/2)

Prove that: sin^2B=sin^2A+sin^2(A-B)-2sin A cos B sin(A-B)

19. Prove that sin(A +B) sin(A-B)+sin(B+C)sin(B-C) + sin(C+A) sin(C-A)=0

CENGAGE ENGLISH-TRIGONOMETRIC FUNCTIONS-All Questions
  1. Let O be the circumcenter, H be the orthocentre, I be the incenter, an...

    Text Solution

    |

  2. If s e c^2theta=(4x y)/((x+y)^2) is true if and only if (a)x+y!=0 (b)...

    Text Solution

    |

  3. Prove that in a A B C ,sin^2A+sin^2B+sin^2C<=9/4dot

    Text Solution

    |

  4. The number of solution of the pair of equations 2sin^2theta-cos2theta=...

    Text Solution

    |

  5. The rational number which equals the number 2. 357 with recurring de...

    Text Solution

    |

  6. If (cos^4A)/(cos^2B)+(sin^4A)/(sin^2B)=1 then prove that (cos^4B)/(cos...

    Text Solution

    |

  7. Prove that r1+r2+r3-r=4R

    Text Solution

    |

  8. Number of solution of equation 2sinx/2cos^2x-2sinx/2sin^2x=cos^2x-sin^...

    Text Solution

    |

  9. If cot(theta-alpha),3cottheta,"cot"(theta+alpha) are in A.P. and theta...

    Text Solution

    |

  10. If x=sectheta-tanthetaa n dy=cos e ctheta+cottheta, then prove that x...

    Text Solution

    |

  11. If A >0,B >0a n dA+B=pi/3, the maximum value of tanAtanB is

    Text Solution

    |

  12. Prove that cosA+cosB+cosC=1+r/R

    Text Solution

    |

  13. denote the positive solution of the equation 3+3costheta=2sin^2thetado...

    Text Solution

    |

  14. If (sec^4theta)/a+(tan^4theta)/b=1/(a+b), then prove that |b|lt=|a| .

    Text Solution

    |

  15. Prove that: ((cosA+cos B)/(sinA-sinB))^n+((sinA+sinB)/(cosA-cosB))^n={...

    Text Solution

    |

  16. Prove that ("a c o s"A+b cosB+c cosC)/(a+b+c)=r/Rdot

    Text Solution

    |

  17. Find the number of solution of the equation 1+e^(cot^2x)=sqrt(2|sinx|-...

    Text Solution

    |

  18. If a^2+b^2+2a bcostheta=1,c^2+d^2+2c dcostheta=1 and a c+b d+(a d+b c)...

    Text Solution

    |

  19. If r1=r2+r3+r prove that the triangle is right angled .

    Text Solution

    |

  20. Find the number of solution of theta in [0,2pi] satisfying the equati...

    Text Solution

    |