Home
Class 12
MATHS
Show that the maximum and minimum values...

Show that the maximum and minimum values of `sqrt(a^(2)cos^(2)theta + b^(2)sin^(2) theta) + sqrt(a^(2)sin^(2)theta + b^(2)cos^(2)theta)` are `sqrt(2(a^(2) +b^(2))` and a + b respectively.

Promotional Banner

Topper's Solved these Questions

  • Circular Functions, Identities

    A DAS GUPTA|Exercise Exercise|300 Videos

  • Circles

    A DAS GUPTA|Exercise EXERCISE|122 Videos

  • COMPLEX NUMBERS

    A DAS GUPTA|Exercise EXERCISE|224 Videos

Similar Questions

Explore conceptually related problems

If M and m denotes maximum and minimum value of sqrt(49cos^(2)theta+sin^(2)theta)+sqrt(49sin^(2)theta+cos^(2)theta) then find the value of (M+m) is

The minimum and maximum values of cos theta+2sqrt(2)sin theta is

u=sqrt(a^(2)cos^(2)theta+b^(2)sin^(2)theta)+sqrt(a^(2)sin^(2)theta+b^(2)cos^(2)theta) then the difference between maximum and minimum values of u^(2) is

Find the maximum and minimum value of log_(sqrt(5))(sqrt(2)(sin theta-cos theta)+3 for all theta

The minimum and maximum values of expression y=cos theta(sin theta+sqrt(sin^(2)theta+sin^(2)alpha))

if (cos^(2)theta)/(a)=(sin^(2)theta)/(b) then (cos^(4)theta)/(a)+(sin^(4)theta)/(b)=?

If a cos theta - b sin theta = c, prove that a sin theta + b cos theta = pm sqrt(a^(2) + b^(2) - c^(2)) .

A DAS GUPTA-Circular Functions, Identities -Exercise
  1. If A gt 0, B gt 0 and A + B = pi/3 then find the maximum value of tan...

    Text Solution

    |

  2. Find the minimum value of 9tan^(2)theta + 4cot^(2)theta.

    Text Solution

    |

  3. Show that the maximum and minimum values of sqrt(a^(2)cos^(2)theta + ...

    Text Solution

    |

  4. Find the set of possible values of (tan(x + pi/6))/tan x where x is an...

    Text Solution

    |

  5. Prove that for real x, (tan(x+alpha))/(tan(x-alpha)) where alpha ne pi...

    Text Solution

    |

  6. Show that (sec^(2)theta - tan theta)/(sec^(2)+ tan theta) lies betwe...

    Text Solution

    |

  7. Prove that tan alpha + 2tan 2alpha + 4tan 4alpha + 8cot 8alpha = cot ...

    Text Solution

    |

  8. Find the sum: tan x + 1/2 tan x/2+ 1/2^(2) tan x/2^(2) +.....+1/2^(n-...

    Text Solution

    |

  9. Prove that cosec 2alpha = cot alpha - cot 2alpha. Hence or otherwise ...

    Text Solution

    |

  10. Prove that sum(r=1)^(10) = sin^(2) rpi/18 =5.

    Text Solution

    |

  11. Sum the series: sin alpha - sin 2alpha + sin 3alpha - sin 4alpha + .....

    Text Solution

    |

  12. Find sum(r=1)^(10) cos^(3) rpi/3.

    Text Solution

    |

  13. Sum: sqrt(1 + sin 2alpha) + sqrt(1 + sin 4alpha) + sqrt(1 + sin 6alpha...

    Text Solution

    |

  14. Prove that sin^(2) 12^circ + sin^(2)21^circ + sin^(2)39^circ + sin^(2)...

    Text Solution

    |

  15. If A + B + C = pi, prove that cos A cosec B cosec C + cos B cosec C c...

    Text Solution

    |

  16. Prove that in a triangle ABC, sin^(2)A - sin^(2)B + sin^(2)C = 2sin A...

    Text Solution

    |

  17. Prove that in a triangle ABC, sum (cot B+ cotC)/(tan B + tan C) =1.

    Text Solution

    |

  18. If A +B+C = 180^circ, prove that cos A/2+ cos B/2 +cos C/2 = 4cos (p...

    Text Solution

    |

  19. If alpha + beta- gamma= pi, prove that sin^(2)alpha + sin^(2)beta - s...

    Text Solution

    |

  20. If alpha + beta + gamma = 2 theta, prove that cos theta + cos(theta- ...

    Text Solution

    |