Home
Class 12
MATHS
"if y"="cos"^(-1)((5"cos" x-12 "sin"x)/(...

`"if y"="cos"^(-1)((5"cos" x-12 "sin"x)/(13)),` where
`x in (0,(pi)/(2)) , " then "(dy)/(dx) " is"-`

A

1

B

-1

C

0

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
`y = " cos"^(-1) [(5)/(13) " cos " x - (12)/(13) " sin "x]`
`y = " cos"^(-1) underset("cos"alpha)underset(darr)([(5)/(13))) " cos " x - underset("sin"alpha)underset(darr)((12)/(13)) " sin "x"]"`
`="cos"^(-1) ["cos"(x+alpha)]`
`y= x+alpha " "y^(1) =1`
Promotional Banner

Topper's Solved these Questions

  • MOCK TEST 3

    CAREER POINT|Exercise MATHS|30 Videos

  • MOCK TEST 5

    CAREER POINT|Exercise Part (C) (MATHS)|30 Videos

Similar Questions

Explore conceptually related problems

y=cos^(-1)((5cos x-12sin x)/(13)),wherexin(0,(pi)/(2)) then (dy)/(dx) is.(a)1(b) -1( c) 0 (d) none of these

If y=cos ^(-1) ((3cos x-2sin x )/( sqrt(13))),then (dy)/(dx)=

If 2y=(cot^(-1)((sqrt3 cos x + sin x)/(cos x - sqrt3 sin x)))^(2) , x in (0, pi/2) " then " (dy)/(dx) is equal to

If y = cos^(-1) ((2cos x - 3 sin x)/(sqrt(13))), " then" (dy)/(dx) is equal to

If y = tan^(-1) ((a cos x - b sin x)/(b cos x + a sin x)) " then " (dy)/(dx) = ?

If y=sqrt((1-cos2x)/(1+cos2x)), where 0

If y=sin x+cos x then (dy)/(dx) =

If y=tan^(-1)[(5cos x-12sin x)/(12cos x+5sin x)], then (dy)/(dx)=

If sin (x+y) +cos (x+y) =1,then (dy)/(dx)=

if y=(sin x)^(cos x). Then (dy)/(dx)=

CAREER POINT-MOCK TEST 4-MATHS
  1. The area bounded by the curves y= "sin" x, y= cos x and y-axis in 1 qu...

    Text Solution

    |

  2. The solution of the DE (dy )/(dx) + sqrt ((1 -y ^(2))/( 1- x ^(2))...

    Text Solution

    |

  3. A variable circle having fixed radius 'a' passes through origin and me...

    Text Solution

    |

  4. The chord A B of the parabola y^2=4a x cuts the axis of the parabola a...

    Text Solution

    |

  5. If tangents are drawn to the ellipse x^2+2y^2=2, then the locus of the...

    Text Solution

    |

  6. f(x) = ("tan" x^(5))e^(x^(3)"sgn"x^(7)) " is " -

    Text Solution

    |

  7. "if y"="cos"^(-1)((5"cos" x-12 "sin"x)/(13)), where x in (0,(pi)/(2)...

    Text Solution

    |

  8. lim(x to0) ((1+a^(3))+8e^(1//x))/(1+(1-b^(3))e^(1//x))=2 " then "-

    Text Solution

    |

  9. If veca,vecb,vecc are three mutually perpendicular vectors, then the v...

    Text Solution

    |

  10. A straight line moves so that the sum of the reciprocals of its interc...

    Text Solution

    |

  11. The points (1,1), (0, "sec"^(2) 0), ("cosec"^(2) 0,0 ) are collinear f...

    Text Solution

    |

  12. The equation of a line which passes through point A(1,0,-1) and perper...

    Text Solution

    |

  13. The curve y=ax^(3)+bx^(2)+cx is inclined by 45^(@) to x-axis at origi...

    Text Solution

    |

  14. If x^(2) +ax - 3x-(a+2) = 0 has real and distinct roots, then minimum ...

    Text Solution

    |

  15. i=int(e^(x))/((x+2)){1+(x+2)log(x+2)}dx=

    Text Solution

    |

  16. If R is a relation on N as R= {(1+ x, 1+x^2): x <= 5, X in N} which of...

    Text Solution

    |

  17. Cosnsider the system of equation a(1)x+b(1)y+c(1)z=0, a(2)x+b(2)y+c(...

    Text Solution

    |

  18. A sample of 35 observations has the means 80 and SD. As 4. A second sa...

    Text Solution

    |

  19. If A and B are two square matrices such that B=-A^(-1)BA, then (A+B)...

    Text Solution

    |

  20. Given A=[(1,1,1),(2,4,1),(2,3,1)], B=[(2,3),(3,4)]. Find P such tha...

    Text Solution

    |