Home
Class 12
MATHS
Find the smallest positive number p for ...

Find the smallest positive number p for which the equation `cos (p sin x) = sin (p cos x)` has a solution `x in [0,2pi]`.

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP|Exercise All Questions|15 Videos

  • MATRICES

    RESONANCE DPP|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

Find the smallest positive number p for which the equation cos(p sin x)=sin(p cos x) has a solution x in[0,2 pi].

Find the values of p for which the equation 1+p sin x=p^(2)-sin^(2)x has a solution

The range of values of p for which the equation sin cos^(-1) ( cos( tan^(-1) x)) = p has a solution is

The range of the values of p for which the equation sin cos^(-1)(cos(tan^(-1)x))=p has a solution is

Smallest positive x satisfying the equation sin3x+3cos x=2sin2x(sin x+cos x), is-

The value of p for which the equation 3 " sin"^(2)x + 12 "cos" x - 3 =p has at least one solution are

The number of solutions that the equation sin (cos (sin x))= cos (sin (cos x)) has in [0, (pi)/(2)], is "_____"

The range of values of p for which the equation sin(cos^(-1)(cos^(-1)(cos(tan^(-1)x)))=p has solution is

Prove that sin1>cos(sin1). Also,show that the equation sin(cos(sin x))=cos(sin(cos x)) has only one solution in [0,(pi)/(2)]

Find the number of solution of the equation sqrt(cos 2x+2)=(sin x + cos x) in [0, pi] .

RESONANCE DPP-JEE MAINS-All Questions
  1. Let 3 non-zero distinct real numbers be in A.P. and their squares in...

    Text Solution

    |

  2. In the adjoining figure find that value of a +b if angleDBE = 90^@

    Text Solution

    |

  3. Find the smallest positive number p for which the equation cos (p sin...

    Text Solution

    |

  4. Find the number ways in which 3 men and their wives can be arranged in...

    Text Solution

    |

  5. OABC is a rhombus whose three vertices A,B and C lie on a cricle with ...

    Text Solution

    |

  6. The function f:[-1//2,\ 1//2]->[-pi//2,pi//2\ ] defined by f(x)=s in^(...

    Text Solution

    |

  7. The equation 7xx^(2)-(7pi+22)xx+22pi=0has

    Text Solution

    |

  8. The value of the expression, (log)4((x^2)/4)-2(log)4(4x^4)w h e nx=-2 ...

    Text Solution

    |

  9. If the quadratic equations 3x^2 + ax + 1 = 0 and 2x^2 + bx + 1 = 0 h...

    Text Solution

    |

  10. Let a,b inQ"such that"(39sqrt2-5)/(3-sqrt2)=a+bsqrt2, then

    Text Solution

    |

  11. Range of f(x)=[1/(log(x^(2)+e))]+1/sqrt(1+x^(2)), where [*] denotes gr...

    Text Solution

    |

  12. A person has to buy 4 ice creams. Number of ways he can choose 4 ice...

    Text Solution

    |

  13. If x=(log)k b=(log)b c=1/2(log)c d ,t h e n(log)k d is equal to 6x b. ...

    Text Solution

    |

  14. State True or False :- The product of two rational numbers is always r...

    Text Solution

    |

  15. If f(x)=2x+abs(x),g(x)=1/3(2x-abs(x)) and h(x)=f(g(x)), domain of unde...

    Text Solution

    |

  16. The number of solution of the equation, log(-2x)=2"log"(x+1) is a. zer...

    Text Solution

    |

  17. Prove that 3+2sqrt(5) is irrationals :

    Text Solution

    |

  18. Given the equation of the line 3x-y+z+1=0 and 5x-y+3z=0. Then,which of...

    Text Solution

    |

  19. The number of real solutions of equation x^((log)x2)+x^2=3x is 2 b. 1 ...

    Text Solution

    |

  20. Find interval of values of ' a ' for which one root of equation x^2+a^...

    Text Solution

    |