Home
Class 11
MATHS
If alpha,beta,gamma, in (0,pi/2) , then ...

If `alpha,beta,gamma, in (0,pi/2)` , then prove that `(s i(alpha+beta+gamma))/(sinalpha+sinbeta+singamma)<1`

A

`lt 1`

B

`gt1`

C

1

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS OF COMPOUND ANGLES

    TARGET PUBLICATION|Exercise COMPETITIVE THINKING|101 Videos

  • TRIGONOMETRIC FUNCTIONS OF COMPOUND ANGLES

    TARGET PUBLICATION|Exercise EVALUATION TEST|12 Videos

  • TRIGONOMETRIC FUNCTIONS OF COMPOUND ANGLES

    TARGET PUBLICATION|Exercise EVALUATION TEST|12 Videos

  • STRAIGHT LINE

    TARGET PUBLICATION|Exercise EVALUATION TEST|10 Videos

  • TRIGONOMETRIC FUNCTIONS

    TARGET PUBLICATION|Exercise EVALUATION TEST|10 Videos

Similar Questions

Explore conceptually related problems

If alpha,beta,gamma,in(0,(pi)/(2)), then prove that (si(alpha+beta+gamma))/(sin alpha+sin beta+sin gamma)<1

If alpha + beta+gamma=pi , prove that sin^2 alpha + sin^ beta - sin^2 gamma = 2sinalpha sinbeta cosgamma

If 0ltalphalt pi/2, 0ltbetaltpi/2 and 0ltgammalt pi/2 prove that sin(alpha+beta+gamma) lt sinalpha+sinbeta +sin gamma

If alpha+beta+gamma=2pi then

Given alpha+beta-gamma=pi, prove that sin^(2)alpha+sin^(2)beta-sin^(2)gamma=2sin alpha sin beta cos gamma

Given alpha+beta-gamma=pi, prove that sin^(2)alpha+sin^(2)beta-sin^(2)gamma=2sin alpha sin beta cos gamma

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

cos(alpha-beta)+cos(beta-gamma)+cos(gamma-alpha)=-(3)/(2), prove that cos alpha+cos beta+cos gamma=sin alpha+sin beta+sin gamma=0

Determine the values of alpha ,beta , gamma when [{:( 0, 2beta, gamma),( alpha ,beta, -gamma),( alpha ,-beta, gamma):}] is orthogonal.

If sinalpha+sinbeta+singamma=cosalpha+cosbeta+cosgamma=0 then prove that cos3alpha+cos3beta+cos3gamma=3cos(alpha+beta+gamma)

TARGET PUBLICATION-TRIGONOMETRIC FUNCTIONS OF COMPOUND ANGLES -CRITICAL THINKING
  1. tan""(2pi)/(5)-tan""(pi)/(15)-sqrt3tan""(2pi)/(5)tan""(pi)/(15) is equ...

    Text Solution

    |

  2. If tan A=2 tan B+cot B, then 2 tan (A-B) is equal to

    Text Solution

    |

  3. If alpha,beta,gamma, in (0,pi/2) , then prove that (s i(alpha+beta+gam...

    Text Solution

    |

  4. (1)/(tan 3 A - tan A)- (1)/(cot 3 A - cot A)=

    Text Solution

    |

  5. Show that sin 150^(@) + cos 105^(@) =(1)/(sqrt(5))

    Text Solution

    |

  6. The vlaue of tan 81^(@) - tan 63^(@) - tan 27^(@)+ tan 9^(@) is equ...

    Text Solution

    |

  7. If alpha+beta=pi/2a n dbeta+gamma=alpha, then tanalpha equals 2(tanbet...

    Text Solution

    |

  8. tan ((pi)/(4)+theta) tan ((3pi)/( 4) + theta) is equal to

    Text Solution

    |

  9. tan(100^(@))+tan(125^(@))+tan(100^(@))tan(125^(@))=

    Text Solution

    |

  10. If A+B=225^@ Find cotA/(1+cotA)*cotB(1+cotB)

    Text Solution

    |

  11. The value of (sin(-660^@)tan(1050^@)sec(420^@))/(cos(225^@)cosec(315^@...

    Text Solution

    |

  12. cos ^(2) ((pi)/(4)beta)- sin ^(2) (alpha - (pi)/(4))=

    Text Solution

    |

  13. THe value of cos^2(pi/12)+cos^2(pi/4)+cos^2((5pi)/12) is

    Text Solution

    |

  14. tanalpha=1/7,tanbeta=1/3,t h e ncos2alpha=

    Text Solution

    |

  15. If costheta=1/2(x+1/x) then 1/2(x^2+1/x^2)=

    Text Solution

    |

  16. If sin x+ cos x =1/5 and 0 le x le pi, then tan x is equal to

    Text Solution

    |

  17. If 0 lt x lt pi and cos x + sin x = 1/2, then tan x is

    Text Solution

    |

  18. If : tan((pi)/(4)+theta) - tan((pi)/(4) - theta) =m*tan (ntheta),"then...

    Text Solution

    |

  19. If sec 2 theta =p + tan 2 theta, then the value of sin^(2) theta in ...

    Text Solution

    |

  20. If theta and phi are angles in first quadrant and tantheta=1/7 and sin...

    Text Solution

    |