Home
Class 11
MATHS
If s inalphas inbeta-cosalphacosbeta+1=0...

If `s inalphas inbeta-cosalphacosbeta+1=0,` then prove that `1+cotalphatanbeta=0`

Text Solution

Verified by Experts

Given,
`sinalphasinbeta−cosalphacosbeta+1=0`
=`cosalphacosbeta−sinalphasinbeta=1 `
=` cos(alpha+beta)=1`
so, `(alpha+beta)=0`
now, ` tan(alpha+beta)=0 `
...
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    RD SHARMA|Exercise Solved Examples And Exercises|167 Videos

  • TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES

    RD SHARMA|Exercise Solved Examples And Exercises|193 Videos

Similar Questions

Explore conceptually related problems

Prove that 0!=1

Prove that 0!=1

Prove that (1+x) 0

If sinAsinB-cosAcosB+1=0 then prove that 1+cotAtanB=0

If A=[(0,sin alpha, sinalpha sinbeta),(-sinalpha, 0, cosalpha cosbeta),(-sinalpha sinbeta, -cosalphacosbeta, 0)] then (A) |A| is independent of alpha and beta (B) A^-1 depends only on beta (C) A^-1 does not exist (D) none of these

Ecaluate [{:(cosalphacosbeta,cosalphasinbeta,-sinalpha),(-sinbeta,cosbeta,0),(sinalphacosbeta,sinalphasinbeta,cosalpha):}]

Prove that : cos^(-1)((cosalpha+cosbeta)/(1+cosalphacosbeta))=2\ tan^(-1)(tanalpha/2tanbeta/2)

If1+ sin^@0 = 3sino coso , then prove that tane = 1 or|-

(1+cosalphacosbeta)^2-(cosalpha+cosbeta)^2=

RD SHARMA-TRIGONOMETRIC RATIOS OF COMPOUND ANGLES-Solved Examples And Exercises
  1. If alpha, beta are two different values of x lying between 0 and 2pi ...

    Text Solution

    |

  2. Prove that (tan^2 (2theta)-tan^2 theta)/(1-tan^2 (2theta) tan^2 theta)...

    Text Solution

    |

  3. If s inalphas inbeta-cosalphacosbeta+1=0, then prove that 1+cotalphata...

    Text Solution

    |

  4. If t a nalpha=x+1,tanbeta=x-1, show that 2cot(alpha-beta)=x^2dot

    Text Solution

    |

  5. Find the maximum and minimum values of 7\ costheta+24 s intheta

    Text Solution

    |

  6. Prove that 5costheta+3cos(theta+pi/3)+3 lies between -4a n d10.

    Text Solution

    |

  7. Reduce sqrt(3)sintheta-costheta as a single term consisting sine only

    Text Solution

    |

  8. Express sintheta-costheta\ as cosine of a single expression.

    Text Solution

    |

  9. Find the maximum and minimum values of each of the following trigono...

    Text Solution

    |

  10. Find the maximum and minimum values of each of the following trigon...

    Text Solution

    |

  11. Find the maximum and minimum values of each of the following trigon...

    Text Solution

    |

  12. Find the maximum and minimum values of each of the following trigon...

    Text Solution

    |

  13. Reduce each of the following expressions to the sine or cosine of a ...

    Text Solution

    |

  14. Reduce each of the following expressions to the sine and cosine of a ...

    Text Solution

    |

  15. Reduce each of the following expressions to the sine and cosine of a ...

    Text Solution

    |

  16. . Show that sin100^@- sin 10^@ is positive

    Text Solution

    |

  17. If alpha+beta-gamma=pi and sin^2alpha+sin^2beta-sin^2gamma=lambda sina...

    Text Solution

    |

  18. If x\ costheta=y cos(theta+(2pi)/3)=z cos(theta+(4pi)/3) , then write ...

    Text Solution

    |

  19. Write the maximum and minimum values of 3cos x+4sin x+5.

    Text Solution

    |

  20. Write the maximum value of 12 s intheta-9sin^2\ \ thetadot

    Text Solution

    |