Home
Class 12
MATHS
If sinx+cosx=sqrt(y+1/y) for x in [0,pi]...

If `sinx+cosx=sqrt(y+1/y)` for `x in [0,pi]` , then `x=pi/4` (b) `y=0` `y=1` (d) `x=(3pi)/4`

A

`x=pi//4`

B

`y=0`

C

`y=1`

D

`x=3pi/4`

Text Solution

Verified by Experts

The correct Answer is:
A, C
`y+1/y ge 2`
`rArr sqrt(y+1/y) ge sqrt(2)`
But `sin x+cos x le sqrt(2)`
`rArr y+1/y=2` and `sin x+cos x=sqrt(2)`
`rArr y=1` and `sin (x+pi/4)=1`
`rArr y=1` and `x=pi/4`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC EQUATIONS

    CENGAGE ENGLISH|Exercise Exercises (Linked comprehension type)|20 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE ENGLISH|Exercise Exercises (Numerical value type)|21 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE ENGLISH|Exercise Exercises (Single Correct Answer Type)|90 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise ARCHIVES INTEGER TYPE|1 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE ENGLISH|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

Similar Questions

Explore conceptually related problems

If sinx+cosx=sqrt(y+1/y) for x in [0,pi] , then (a) x=pi/4 (b) y=0 (c) y=1 (d) x=(3pi)/4

If sinx+cosx=sqrt(y+1/y), y gt 0, x in[0,pi] , then find the least value of x satisfying the given conditions.

If x^2-4x+5-siny=0, yepsilon [0,2pi] then (A) x=1,y=0 (B) x=1,y=pi/2 (C) x=2,y=0 (D) x=2,y=pi/2

If xa n dy are positive acute angles such that (x+y) and (x-y) satisfy the equation tan^2theta-4tantheta+1=0, then x=pi/6 (b) y=pi/4 (c) y=pi/6 (d) y=pi/4

If xa n dy are positive acute angles such that (x+y) and (x-y) satisfy the equation tan^2theta-4tantheta+1=0, then x=pi/6 (b) y=pi/4 (c) y=pi/6 (d) y=pi/4

If ( sin x) (cos y) = 1//2, then d^(2)y//dx^(2) at (pi//4, pi//4) is

f(x)=sin+sqrt(3)cosx is maximum when x= pi/3 (b) pi/4 (c) pi/6 (d) 0

If (sinx)(cosy)=1/2, then (d^2y)/(dx^2) at (pi/4,pi/4) is (a) -4 (b) -2 (c) -6 (d) 0

The equation of the normal to the curve x=a\ cos^3theta,\ \ y=a\ sin^3theta at the point theta=pi//4 is (a) x=0 (b) y=0 (c) x=y (d) x+y=a

The function f(x)=tan^(-1)(sinx+cosx) is an increasing function in (-pi/2,pi/4) (b) (0,pi/2) (-pi/2,pi/2) (d) (pi/4,pi/2)

CENGAGE ENGLISH-TRIGONOMETRIC EQUATIONS-Exercises (Multiple correct type)
  1. If sin^(3) theta+sin theta cos theta+ cos^(3) theta=1, then theta is e...

    Text Solution

    |

  2. A general solution of tan^(2) theta+ cos 2 theta=1 is (n in Z)

    Text Solution

    |

  3. If sinx+cosx=sqrt(y+1/y) for x in [0,pi] , then x=pi/4 (b) y=0 y=1 ...

    Text Solution

    |

  4. The equation 2 sin^(2) (pi/2 cos^(2) x)=1-cos (pi sin 2x) is safisfied...

    Text Solution

    |

  5. If sin^2x-2sinx-1=0 has exactly four different solutions in x in [0,np...

    Text Solution

    |

  6. For the smallest positive values of xa n dy , the equation 2(s inx+s i...

    Text Solution

    |

  7. For the equation 1-2x-x^2=tan^2(x+y)+cot^2(x+y) exactly one value of ...

    Text Solution

    |

  8. If x+y=pi//4 and tan x+tan y=1, then (n in Z)

    Text Solution

    |

  9. If x+y=2pi//3 and sin x//sin y=2, then the

    Text Solution

    |

  10. Let tanx-tan^2x >0 and |2sinx|<1 . Then the intersection of which of t...

    Text Solution

    |

  11. If cos(x+pi/3)+cos x=a has real solutions, then number of integral val...

    Text Solution

    |

  12. If 0 le x le 2pi, then 2^(cosec^(2) x) sqrt(1/2 y^(2) -y+1) le sqrt(2...

    Text Solution

    |

  13. If the equation sin^2 x-a sin x + b = 0 has only one solution in (0, p...

    Text Solution

    |

  14. If (cos e c^2theta-4)x^2+(cottheta+sqrt(3))x+cos^2(3pi)/2=0 holds true...

    Text Solution

    |

  15. If (sinalpha)x^2-2x+bgeq2, for all real values of xlt=1a n dalpha in (...

    Text Solution

    |

  16. The value of x in (0,pi/2) satisfying the equation, (sqrt3-1)/sin x+ (...

    Text Solution

    |

  17. If cos3theta=cos3alpha, then the value of sintheta can be given by +-s...

    Text Solution

    |

  18. Which of the following sets can be the subset of the general solution ...

    Text Solution

    |

  19. The values of x1 between 0 and 2pi , satisfying the equation cos3x+cos...

    Text Solution

    |

  20. Which of the following set of values of x satisfies the equation 2^((2...

    Text Solution

    |