Home
Class 11
MATHS
If alpha+beta=90^0 , find the maximum a...

If `alpha+beta=90^0` , find the maximum and minimum values of `sinalphasinbetadot`

Text Solution

Verified by Experts

Given,
`alpha+beta=90`
Let take
`y=sinalphasinbeta`
Then,
`=>y=(1/2)(2sinalphasinbeta)`
`=(1/2)[cos(alpha−beta)−cos(alpha+beta)]`
`=(1/2)[cos(alpha−beta)−cos90^@]`
`=(1/2)cos(alpha−beta)`
...
Promotional Banner

Topper's Solved these Questions

  • THE STRAIGHT LINES

    RD SHARMA|Exercise Solved Examples And Exercises|488 Videos

  • TRIGONOMETRIC EQUATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|120 Videos

Similar Questions

Explore conceptually related problems

If alpha+beta=90^(0) ,then the minimum and maximum values of cos alpha*cos beta are (A) -1/3 and 1/3 (B) -1 and 1 (C) -1/4 and 1/4 (D) -1/2 and 1/2

If Z+alpha|Z-1|+2i=0 , then find the sum of maximum and minimum values of alpha .( alpha in R )

The minimum values of (x-alpha)(x-beta) is

The minimum value of (x-alpha)(x-beta) is

If alpha+beta=90^(0) ,show that the maximum value of cos alpha.cos beta is (1)/(2)

If alpha+beta=90^@ , show that the maximum value of cos alpha cos beta is (1)/(2)

If alpha and beta are the real roots of the equation x^(2)-(k-2)x+(k^(2)+3k+5)=0,(k in R) Then the maximum and minimum values of alpha^(2)+beta^(2)

If alpha+beta=90^(@),alpha=2beta , then find the value of cos^(2)alpha+sin^(2)beta .

If alpha+beta=90^@ and alpha=2beta , then the value of 3cos^2alpha-2sin^2beta is equal to:

RD SHARMA-TRANSFORMATION FORMULAE-Solved Examples And Exercises
  1. Prove that :"sin"Asin(60^0-A)sin(60^0+A)=1/4sin3A

    Text Solution

    |

  2. Show that: t a n(60^0+theta)t a n(60^0-theta)=(2cos2theta+1)/(2cos2the...

    Text Solution

    |

  3. If alpha+beta=90^0 , find the maximum and minimum values of sinalphas...

    Text Solution

    |

  4. Prove that: cos20^0cos40^0cos60^0cos80^0=1/(16)

    Text Solution

    |

  5. Prove that: sin20^0sin40^0sin60^0sin80^0=3/(16)

    Text Solution

    |

  6. Prove that: 4"cos"12^0cos48^0cos72^0=cos36^0

    Text Solution

    |

  7. Prove that: t a nthetatan(60^0-theta)tan(60^0+theta)=tan3thetadot

    Text Solution

    |

  8. Prove that: sin(B-C)cos(A-D)+sin(C-A)cos(B-D)+sin(A-B)cos(C-D)=0

    Text Solution

    |

  9. If sinx+siny=sqrt(3)(cos y-cos x), then sin3x+sin3y= (a)2sin3x (...

    Text Solution

    |

  10. Prove that: (cos(A+B+C)+cos(-A+B+C)+cos(A-B+C)+"cos"(A+B-C))/(sin(A+B...

    Text Solution

    |

  11. Prove that: ((cosA+cos B)/(sinA-sinB))^n+((sinA+sinB)/(cosA-cosB))^n=...

    Text Solution

    |

  12. If sintheta=n"sin"(theta+2alpha) , prove that tan(theta+alpha)=(1+n)/...

    Text Solution

    |

  13. Prove that: (sin(A-C)+2sinA+sin(A+C)) / ("sin"("B"-"C")+2sinB+"sin"(B+...

    Text Solution

    |

  14. Prove that: ("cos"8Acos5A-cos12 Acos9A)/("sin"8Acos5A+cos12 As in9A)=t...

    Text Solution

    |

  15. Prove that: (sinA+sin3A+sin5A+sin7A)/(cosA+cos3A+cos5A+cos7A)=tan4A

    Text Solution

    |

  16. Prove that: 1+cos2x+cos4x+cos6x=4cosxcos2xcos3x

    Text Solution

    |

  17. Prove that: cos18^0-si n 18^0=sqrt(2)sin27^0

    Text Solution

    |

  18. Express each of the following as a product: sin4theta+sin2theta (ii) ...

    Text Solution

    |

  19. If (sin(theta+alpha))/(cos(theta-alpha))=(1-m)/(1+m) , prove that tan(...

    Text Solution

    |

  20. If sintheta+sinphi=sqrt3(cosphi-costheta)) , prove that sin3theta+sin...

    Text Solution

    |