Home
Class 12
MATHS
If alpha+beta=pi/2a n dbeta+gamma=alpha,...

If `alpha+beta=pi/2a n dbeta+gamma=alpha,` then `tanalpha` equals `2(tanbeta+tangamma)` (b) `tanbeta+tangamma` `tanbeta+2tangamma` (d) `2tanbeta+tangamma`

A

`2(tanbeta+tangamma)`

B

`tanbeta+tangamma`

C

`tan beta+2 tangamma`

D

`2tanbeta+tangamma`

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`beta+gamma+alpha`
`impliesgamma=alpha=beta`
`tangamma=tan(alpha-beta)`
`impliestangamma=(tanalpha-tanbeta)/(1+tanalphatanbeta)`
`impliestangamma=(tanalpha-tanbeta)/(1+tanalphacot alpha)" "[becausealpha+beta=(pi)/(2)becausebeta=(pi)/(2)-alpha]`
`impliestangamma=1/2(tangamma-tanbeta)impliestanalpha=tanbeta+2tangamma.`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND IDENTITIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|13 Videos

  • TRIGONOMETRIC RATIOS AND IDENTITIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|189 Videos

  • TRIGONOMETRIC RATIOS AND IDENTITIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|60 Videos

  • TRIGONOMETRIC EQUATIONS AND INEQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|60 Videos

Similar Questions

Explore conceptually related problems

If alpha + beta = 90^@ and beta + gamma = alpha then tanalpha-tanbeta=?

If tanalpha+tanbeta+tangamma=tanalphatanbetatangamma,then

Let alpha=som^(-1)((36)/(85)),beta=cos^(-1)(4/5)a n dgamma=tan^(-1)(8/(15)) then cotalpha+cotbeta+cotgamma=cotalphacotbetacotgamma tanalphatanbeta+tanbetatangamma+tanalphatangamma=1 tanalpha+tanbeta+tangamma=tanalphatanbetatangamma cotalphacotbeta+cotbetacotgamma+cotalphacotgamma=1

Let alpha,betaa n dgamma be some angles in the first quadrant satisfying tan(alpha+beta)=(15)/8a n dcos e cgamma=(17)/8, then which of the following hold(s) good? (a) alpha+beta+gamma=pi (b) cotalpha+cotbeta+cotgamma=cotalphacotbetacotgamma (c) tanalpha+tanbeta+tangamma=tanalphatanbetatangamma (d) tanalphatanbeta+tanbetatangamma+tangammatanalpha=1

If alpha+beta+gamma=2pi, then (a) tan(alpha/2)+tan(beta/2)+tan(gamma/2)=tan(alpha/2)tan(beta/2)tan(gamma/2) (b) tan(alpha/2)tan(beta/2)+tan(beta/2)tan(gamma/2)+tan(gamma/2)tan(alpha/2)=1 (c) tan(alpha/2)+tan(beta/2)+tan(gamma/2)=-tan(alpha/2)tan(beta/2)tan(gamma/2) (d)none of these

If alpha+beta+gamma=2pi , then show that tan.alpha/2 + tan.beta/2 + tan.gamma/2 = tan.alpha/2 tan.beta/2 tan.gamma/2 .

If tanbeta = costheta*tanalpha , then tan^2(theta/2) is equal to

If tangamma=secalpha secbeta+tanalphatanbeta, then cos2 gamma is necessarily

if 0ltalphaltbetaltgammaltpi/ 2, then prove that tanalpha lt (sinalpha+sinbeta+singamma)/ (cosalpha+cosbeta+cosgamma)lt tangamma

If tan(alpha-beta)=(sin2beta,)/(3-cos2beta) then (a) tanalpha=2tanbeta (b) tanbeta=2tanalpha (c) 2tanalpha=3tanbeta (d) 3tanalpha=2tanbeta

OBJECTIVE RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS AND IDENTITIES-Section I - Solved Mcqs
  1. For a positive integer n , let fn(theta)=(tantheta//2)(1+sectheta)(1+s...

    Text Solution

    |

  2. Let f(theta)=sintheta(sintheta+sin3theta)dot Then f(theta)i s geq0on ...

    Text Solution

    |

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

    Text Solution

    |

  4. If 5 (tan ^(2) x - cos ^(2) x ) = 2 cos 2x +9, then the value of cos 4...

    Text Solution

    |

  5. Let alpha and beta be non-zero real numbers such that 2 ( cos beta -...

    Text Solution

    |

  6. The maximum value of (cos alpha(1))(cos alpha(2))... ( cos alpha(n)) u...

    Text Solution

    |

  7. Prove that tanpi/(16)+2tanpi/8+4=cotpi/(16) .

    Text Solution

    |

  8. If sin A=a cos B and cosA=b sinB then, (a^2 - 1) tan^2 A+(1 -b^2)ta...

    Text Solution

    |

  9. If (pi)/(2)lt thetalt(3pi)/(2),then sqrt((1-sintheta)/(1+sintheta))"is...

    Text Solution

    |

  10. If cos^(4)theta sec^(2)alpha, 1/2 and sin^(4)theta cosec^(2) alpha ar...

    Text Solution

    |

  11. If 4 n alpha= pi, then cot alpha cot 2alpha cot 3alpha...cot( 2n-1)alp...

    Text Solution

    |

  12. If sinx+sin^2x+sin^3x=1 then find the value of cos^6x-4cos^4x+8cos^2x

    Text Solution

    |

  13. If theta=pi/(2^n+1) , prove that: 2^ncosthetacos2thetacos2^2 cos2^(n-1...

    Text Solution

    |

  14. If A+B=pi/3" where "A, B gt 0, then minimum value of sec A + sec B is ...

    Text Solution

    |

  15. If cos(theta - alpha) , costheta , cos(theta + alpha) are in H.P. then...

    Text Solution

    |

  16. If asintheta="bsin"(theta+(2pi)/3)="csin"(theta+(4pi)/3) , prove that ...

    Text Solution

    |

  17. If 2 sin alpha cos beta sin gamma=sin beta sin( alpha-gamma). Then, s...

    Text Solution

    |

  18. If cos 5 theta = a cos^(5)theta + b cos^(3)theta+c cos theta. Then, fi...

    Text Solution

    |

  19. Given tan A and tan B are the roots of x^2-ax + b = 0, The value of si...

    Text Solution

    |

  20. The value of sin^(6)((pi)/(49))+cos^(6)((pi)/(49))-1+3sin^(2)((pi)/(...

    Text Solution

    |