Home
Class 11
MATHS
If 2tanalpha=3t a nbeta,t h e ntan(alpha...

If `2tanalpha=3t a nbeta,t h e ntan(alpha-beta)=` `(a)(sin2beta)/(5-cos2beta)` (b) `(cos2beta)/(5-cos2beta)` (c) `(sin2beta)/(5+cos2beta)` (d) none of these

Text Solution

Verified by Experts

Given,`2tanalpha=3t a nbeta`
`L.H.S=tan(alpha-beta)=(tan(alpha)-tan(beta))/(1+tan alpha tan beta)`
=`(3/2xxtan(beta)-tan(beta))/(1+3/2xxtan^2 beta)`
=`(1/2xxtan(beta))/(1+3/2xxtan^2 beta)`
=`(tan(beta))/(2+3tan^2 beta)`
=`(sin(beta)/cos(beta))/(2+3(sin^2(beta)/cos^2(beta)))`
=`(sin(beta)xxcos^2(beta)/cos(beta))/(2cos^2(beta)+3(sin^2(beta)))`
=`(sin(beta)xxcos(beta))/(2cos^2(beta)+2sin^2(beta)+sin^2(beta))`
...
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS OF COMPOUND ANGLES

    RD SHARMA|Exercise Solved Examples And Exercises|149 Videos

Similar Questions

Explore conceptually related problems

If 2tan alpha=3tan beta, prove that tan(alpha-beta)=(sin2 beta)/(5-cos2 beta)

If 2tan alpha=3tan beta, prove that tan(alpha-beta)=(sin2 beta)/(5-cos2 beta)

If tan (alpha-beta)=(sin 2beta)/(3-cos 2beta) , then

If 2(tan alpha)/(2)=(tan beta)/(2), prove that cos alpha=(3+5cos beta)/(5+3cos beta)

If 2tan(alpha)/(2)=tan((beta)/(2)), prove that cos alpha=(3+5cos beta)/(5+3cos beta)

tan (alpha + beta) tan (alpha-beta) = (sin ^ (2) alpha-sin ^ (2) beta) / (cos ^ (2) alpha-sin ^ (2) beta)

If cos (alpha+beta)=0 , then sin(alpha-beta) canbe reduced to : (a) cosbeta (b) cos2beta ( c) sinalpha (d) sin2alpha

If cot(alpha+beta)=0, then sin(alpha+2 beta) can be (a)-sin alpha(b)sin beta(c)cos alpha(d)cos beta

If cos^2alpha-sin^2alpha=tan^2beta," then prove that "tan^2alpha=cos^2beta-sin^2beta .

If cos(alpha+beta)=0 then sin^(2)alpha+sin^(2)beta

RD SHARMA-TRIGONOMETRIC RATIOS OF MULTIPLE AND SUBMULTIPLE ANGLES-Solved Examples And Exercises
  1. If tantheta=a/b ,then bcos2theta+asin2theta is equal to (a) a (b) b ...

    Text Solution

    |

  2. Prove that: cos^2A+cos^2(A+(2pi)/3)+cos^2(A-(2pi)/3)=3/2

    Text Solution

    |

  3. If 2tanalpha=3t a nbeta,t h e ntan(alpha-beta)= (a)(sin2beta)/(5-cos2...

    Text Solution

    |

  4. Prove that: sin^2 24^@-sin^2 6^@=(sqrt(5)-1)/8

    Text Solution

    |

  5. What is the value of cos36^@ .

    Text Solution

    |

  6. Prove that: sin^2 24^0-sin^2 6^0=(sqrt(5)-1)/8

    Text Solution

    |

  7. Prove that: cos18^0=(sqrt(10+2sqrt(5)))/4 .

    Text Solution

    |

  8. If t a ntheta/2=sqrt((1-e)/(1+e))tan(alpha/2), then cosalpha= (a) 1-...

    Text Solution

    |

  9. If cos2x+2cosx=1t h e n ,(2-cos^2x)sin^2x is equal to

    Text Solution

    |

  10. If alphaa n dbeta are acute angles satisfying cos2alpha=(3cos2beta-1)/...

    Text Solution

    |

  11. Prove that: cos^2A+cos^2(A+pi/3)+cos^2(A-pi/3)=3/2

    Text Solution

    |

  12. Prove that: cos^(2)48^(@)-sin^(2)12^(@)=(sqrt(5)+1)/(8)

    Text Solution

    |

  13. The value of (sin5alpha-sin3alpha)/(cos5alpha+2cos4alpha+cos3alpha) is

    Text Solution

    |

  14. If costheta=1/2(a+1/a),cos3theta=lambda(a^3+1/(a^3)),t h e nlambda= ...

    Text Solution

    |

  15. Prove that: t a nA+tan(60^0+A)-t a n(60^0-A)=3t a n3A

    Text Solution

    |

  16. If t a n^2theta=2tan^2phi+1 , prove that cos2theta+sin^2phi=0.

    Text Solution

    |

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

    Text Solution

    |

  18. Prove that: cotA+"cot"(60^0+A)-cot(60^0-A)=3cot3A

    Text Solution

    |

  19. Prove that: cos^2 48^0-sin^2 12^0=(sqrt(5)+1)/8

    Text Solution

    |

  20. Find sin x/2 ,cos x/2 and tan x/2 of the following : tanx=-4/3,""x in...

    Text Solution

    |