Home
Class 11
MATHS
If 3sinbeta=sin(2alpha+beta) then tan(a...

If `3sinbeta=sin(2alpha+beta)` then `tan(alpha+beta)-2tanalpha` is (a)independent of `alpha` (b)independent of `beta` (c)dependent of both `alpha` and `beta` (d)independent of both `alpha` and `beta`

Text Solution

Verified by Experts

`tan(alpha+beta) - 2tanalpha`
`= sin(alpha+beta)/cos(alpha+beta) - sinalpha/cosalpha - tanalpha`
`=(sin(alpha+beta)cosalpha - sinalphacos(alpha+beta))/(cosalphacos(alpha+beta)) - tanalpha`
`=(sin(alpha+beta-alpha))/(cosalphacos(alpha+beta)) - sinalpha/cosalpha`
`=(sinbeta)/(cosalphacos(alpha+beta)) - sinalpha/cosalpha`
`=(sinbeta - sinalphacos(alpha+beta))/(cosalphacos(alpha+beta)) `
`=(2(sinbeta - sinalphacos(alpha+beta)))/(2cosalphacos(alpha+beta)) `
`=(2sinbeta - 2sinalphacos(alpha+beta))/(2cosalphacos(alpha+beta)) `
...
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise All Questions|486 Videos

Similar Questions

Explore conceptually related problems

If. b sin beta = a sin (2alpha +beta) then the.value of cot(alpha+beta)/cotalpha

If tan 2alpha = cot 2beta , then sec(alpha + beta) =

If "cot"(alpha+beta)=0, then "sin"(alpha+2beta) can be

If sin 2 alpha = 4 sin 2 beta, "show that", 5tan ( alpha -beta) = 3 tan ( alpha +beta)

"If " sin2 alpha = A sin 2(alpha + beta), A ne 0, "then "tan 2 beta=

If b sin alpha = alphasin (alpha+2beta),"show that"(b+a) tan beta=(b-a)tan (alpha+beta)

If sin(alpha + beta) = 4/5 and sin (alpha - beta)= 5/13 , find the value of tan 2 alpha .

Prove that (cos2 alpha-cos 2 beta)/(sin2 alpha+sin2 beta)=tan(beta-alpha)

Find the value of (sin (alpha + beta))/(sin (alpha - beta)), "given that" tan alpha = 2 tan beta.

If 3 sinalpha=5sin beta , then find the value of ("tan"(alpha+beta)/2)/("tan"(alpha-beta)/2)

CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS-All Questions
  1. The expression cos3theta+sin3theta+(2sin2theta-3)(sintheta-costheta) i...

    Text Solution

    |

  2. There exists a triangle A B C satisfying the conditions (A) bsinA = ...

    Text Solution

    |

  3. If 3sinbeta=sin(2alpha+beta) then tan(alpha+beta)-2tanalpha is ...

    Text Solution

    |

  4. The number of all possible values of θ where 0 < θ < π, for which the ...

    Text Solution

    |

  5. A straight line through the vertex P of a triangle P Q R intersects th...

    Text Solution

    |

  6. Match the statements/expressions in Column I with the statements/ex...

    Text Solution

    |

  7. x=sqrt(a^(2)cos^(2)alpha+b^(2)sin^(2)alpha)+sqrt(alpha^(2)sin^(2)alpha...

    Text Solution

    |

  8. Which of the following expresses the circumference of a circle inscr...

    Text Solution

    |

  9. Match the statement/expressions in Column I with the statements/expres...

    Text Solution

    |

  10. If (x-a)costheta+ysintheta=(x-a)cosphi+ysinphi=a and tan(theta/2)-tan(...

    Text Solution

    |

  11. Prove that (b + c) cos A + (c + a) cos B + (a + b) cos C = 2s

    Text Solution

    |

  12. If p=sin(A-B)sin(C-D),q=sin(B-C)sin(A-D), r=sin(C-A)sin(B-D) then (...

    Text Solution

    |

  13. Let varphi,phi in [0,2pi] be such that 2costheta(1-sinphi)=sin^2theta(...

    Text Solution

    |

  14. If cos(A/2)=sqrt((b+c)/(2c)) , then prove that a^2+b^2=c^2dot

    Text Solution

    |

  15. If cosx-sinalphacotbetasinx=cosa , then the value of tan(x/2) is (a...

    Text Solution

    |

  16. For 0ltthetaltpi/2 the solution of underset (m=1)overset6sumcosec(thet...

    Text Solution

    |

  17. In A B C ,if a=10 and bcotB+ c cotC=2(r+R) then the maximum area of ...

    Text Solution

    |

  18. Which of the following set of values of x satisfies the equation 2^(2...

    Text Solution

    |

  19. Let f(x)=a bsinx+bsqrt(1-a^2)cosx+c , where |a|<<1,b>>0 then (a) ma...

    Text Solution

    |

  20. A variable triangle A B C is circumscribed about a fixed circle of uni...

    Text Solution

    |