Home
Class 11
MATHS
If alpha in (0,pi/2), then sqrt(x^2+x)...

If `alpha in (0,pi/2)`, then `sqrt(x^2+x)+tan^2alpha/sqrt(x^2+x)` is always greater than or equal to (a) `2tanalpha` (b)1 (c) 2 (d) `sec2alpha`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise All Questions|9 Videos
  • STRAIGHT LINES

    CENGAGE ENGLISH|Exercise All Questions|491 Videos

Similar Questions

Explore conceptually related problems

If (pi)/(2)lt alpha lt (3pi)/(4) , then sqrt(2tan alpha+(1)/(cos^(2)alpha)) is equal to

Let a in (0,(pi)/(2)) and f(x)=sqrt(x^(2)+x)+(tan^(2)alpha)/(sqrt(x^(2)+x)), x gt 0 . If the least value of f(x) is 2sqrt3 , then alpha is equal to

If n=pi/(4alpha), then tan alpha tan 2alpha tan 3 alpha ... tan(2n-1)alpha is equal to (a) 1 (b) 1/2 (c) 2 (d) 1/3

If u=cot^-1 sqrt(tanalpha)-tan^-1 sqrt(tan alpha), then tan(pi/4-u/2) is equal to (a) sqrt(tan alpha) (b) sqrt(cos alpha) (c) tan alpha (d) cot alpha

If u=cot^-1 sqrt(tanalpha)-tan^-1 sqrt(tan alpha), then tan(pi/4-u/2) is equal to (a) sqrt(tan alpha) (b) sqrt(cos alpha) (c) tan alpha (d) cot alpha

If alpha is an acute angle and sin(alpha/2)=sqrt((x-1)/(2x)) then tan alpha is

If 0 < alpha < pi/6 and sin alpha + cos alpha =sqrt(7 )/2, then tan alpha/2 is equal to

If cos^(-1)x-cos^(-1)y/2=alpha,t h e n4x^2-4x ycosalpha+y^2 is equal to 4 (b) 2sin^2alpha (c) -4sin^2alpha (d) 4sin^2alpha

If alpha, betaepsilon(0, pi/2) and if sin^4alpha+4cos^4beta+2=4sqrt2 sinalphacosbeta then the value of cos(alpha+beta)-cos(alpha-beta) is (A) sqrt2 (B) 1/sqrt2 (C) -1/sqrt2 (D) -sqrt2

Let alpha in (0, pi/2) be fixed. If the integral int(tan x + tan alpha)/(tan x - tan alpha)dx = A(x)cos 2 alpha+B(x) sin 2 alpha +C ,where C is a constant of integration, then the functions A(x) and B(x) are respectively.

CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
  1. If a ,b ,c ,d are positive real umbers such that a+b+c+d=2,then M=(a+...

    Text Solution

    |

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

    Text Solution

    |

  3. If alpha in (0,pi/2), then sqrt(x^2+x)+tan^2alpha/sqrt(x^2+x) is alw...

    Text Solution

    |

  4. In A B C , prove that cos e c A/2+cos e c B/2+cos e c C/2geq6.

    Text Solution

    |

  5. In Delta A B C , prove that t a n A+t a n B+t a n Cgeq3sqrt(3),w h e...

    Text Solution

    |

  6. If a ,b ,c are real numbers such that 0 < a < 1,0 < b < 1,0 < c < 1,a+...

    Text Solution

    |

  7. If a^2+b^2+c^2=x^2+y^2+z^2=1, then show that a x+b y+c z leq1.

    Text Solution

    |

  8. Prove that a^4+b^4+c^4> a b c(a+b+c),w h e r ea ,b ,c > 0.

    Text Solution

    |

  9. Prove that the greatest value of x y is c^3/sqrt(2a b), if a^2x^4+b^2y...

    Text Solution

    |

  10. If a > b and n is a positive integer, then prove that a^n-b^n > n(a b)...

    Text Solution

    |

  11. If y = sin^-1(10x) + pi/2 then find the value of dy/dx .

    Text Solution

    |

  12. If a+b=1,a >0, prove that (a+1/a)^2+(b+1/b)^2geq(25)/2dot

    Text Solution

    |

  13. If Cr=(n !)/([r !(n-r)]), the prove that sqrt(C1)+sqrt(C2)+.......sq...

    Text Solution

    |

  14. If x and y are positive real numbers and m, n are any positive integ...

    Text Solution

    |

  15. The least value of the expression 2(log)(10)x-(log)x(0. 01),forx >1, i...

    Text Solution

    |

  16. If a , b , c , are positive real numbers, then prove that (2004, 4M) {...

    Text Solution

    |

  17. True / False For every intger n >1 , the inequality (n !)^(1//n)<(n+1)...

    Text Solution

    |

  18. If x ,y in R^+ satisfying x+y=3, then the maximum value of x^2y is.

    Text Solution

    |

  19. For anyx ,y , in R^+,x y >0 . Then the minimum value of (2x)/(y^3)+(x...

    Text Solution

    |

  20. If a ,b ,a n dc are positive and 9a+3b+c=90 , then the maximum value o...

    Text Solution

    |