Home
Class 12
MATHS
Prove that tan(alpha+beta)=(tanalpha+tan...

Prove that `tan(alpha+beta)=(tanalpha+tanbeta)/(1-tanalphatanbeta)`

Text Solution

Verified by Experts

The following figure is self-explanatory.
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise 2.1|8 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise Exercise 2.2|8 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE|Exercise Archives (Matrix Match Type)|1 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Matrix Match Type|1 Videos

Similar Questions

Explore conceptually related problems

(1+tanalphatanbeta)^2+(tanalpha-tanbeta)^2=

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

Prove that cos(alpha+beta )=cosalphacosbeta-sinalphasinbeta

If tan beta=cos theta tan alpha , then prove that tan^(2)""(theta)/(2)=(sin(alpha-beta))/(sin(alpha+beta)) .

Prove that sin4 alpha=4tan alpha (1- tan^(2)alpha)/((1+tan^2 alpha)^2

Prove that |cosalpha-cosbeta|lt=|alpha-beta|

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? alpha+beta+gamma=pi cotalpha+tanbeta+tangamma=tanalphatanbetatangamma tanalpha+tanbeta+tangamma=tanalphatanbetatangamma tanalphatanbeta+tanbetatangamma+tangammatanalpha=1

Prove that sin 4alpha = 4 tan alpha (1 - tan^(2) alpha)/((1 + tan^(2) alpha)^(2))

If cosx-sinalphacotbetasinx=cosa , then the value of tan(x/2) is -tan(alpha/2)cot(beta/2) (b) tan(alpha/2)tan(beta/2) -cot((alphabeta)/2)tan(beta/2) (d) cot(alpha/2)cot(beta/2)

CENGAGE-TRIGONOMETRIC FUNCTIONS -SINGLE CORRECT ANSWER TYPE
  1. Prove that tan(alpha+beta)=(tanalpha+tanbeta)/(1-tanalphatanbeta)

    Text Solution

    |

  2. The circular wire of diameter 10 cm is cut and placed along the circum...

    Text Solution

    |

  3. sintheta/(1-cottheta)+costheta/(1-tantheta)= (a)theta (b)1 (c)costh...

    Text Solution

    |

  4. If theta in (pi//4, pi//2) and sum(n=1)^(oo)(1)/(tan^(n)theta)=sin the...

    Text Solution

    |

  5. The value of (tan^(2)20^(@)-sin^(2)20^(@))/(tan^(2)20^(@).sin^(2)20^(@...

    Text Solution

    |

  6. If 15 sin^(4)alpha+10cos^(4)alpha=6, then the value of 8 cosec^(6)alph...

    Text Solution

    |

  7. In DeltaABC, if sin A + sin B + sin C= 1 + sqrt2 and cos A+cos B+cos...

    Text Solution

    |

  8. If (sin^(2)x-2cos^(2)x+1)/(sin^(2)x+2cos^(2)x-1)=4, then the value of ...

    Text Solution

    |

  9. If sintheta,tantheta,costheta are in G.P. then 4sin^2theta-3sin^4theta...

    Text Solution

    |

  10. If tantheta-cottheta=aandsintheta+costheta=b(b^2-1)^2(a^2+4) is equal...

    Text Solution

    |

  11. The least value of 18 sin^(2)theta+2 cosec^(2)theta-3 is

    Text Solution

    |

  12. If tan^2 alpha tan^2 beta + tan^2 beta tan^2 gamma + tan^2 gamma tan^2...

    Text Solution

    |

  13. If x,y,z be all positive acute angles then the least value of tanx(cot...

    Text Solution

    |

  14. Three circles each of radius 1, touch one another externally and they ...

    Text Solution

    |

  15. If (cos alpha)/(cos A)+(sin alpha)/(sin A)+(sin beta)/(sin A)=1, where...

    Text Solution

    |

  16. Consider angles alpha = (2n+(1)/(2))pi pm A and beta = m pi +(-1)^(m)(...

    Text Solution

    |

  17. Which of the following is true ?

    Text Solution

    |

  18. If the angle A of a triangle ABC is given by the equation 5 cos A + 3 ...

    Text Solution

    |

  19. Which of the following is greatest ?

    Text Solution

    |

  20. The number of value/values of x for which sin y=x^(2)-2x si possible i...

    Text Solution

    |

  21. Which of the following is not correct ?

    Text Solution

    |