Home
Class 12
MATHS
If f(x)=|{:(sectheta," "tan^(2)theta,1),...

If `f(x)=|{:(sectheta," "tan^(2)theta,1),(thetasecx," "tanx,x),(" "1,tanx-tantheta,0):}|`, then `f'(theta)` is

A

0

B

-1

C

independent of `theta`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`f(x)=|{:(sectheta," "tan^(2)theta,1),(thetasecx," "tanx,x),(" "1,tanx-tantheta,0):}|`
`f(x)=|{:(0," "0,0),(thetasecx," "tanx,x),(" "1,tanx-tantheta,0):}|+|{:(sectheta," "tan^(2)theta,1),(thetasecxtanx," "sec^(2)x,1),(" "1,tanx-tantheta,0):}|+|{:(sectheta," "tan^(2)theta,1),(thetasecx," "tanx,x),(" "0," "sec^(2)x,0):}|`
`:.f'(theta)=0+|{:(sectheta," "tan^(2)theta,1),(thetasecthetatantheta," "sec^(2)theta,1),(" "1," "0,0):}|+|{:(sectheta," "tan^(2)theta,1),(thetasectheta," "tantheta,theta),(" "0," "sec^(2)theta,0):}|`
`impliesf'(theta)=tan^(2)theta-sec^(2)theta+sec^(2)theta(thetasectheta-thetasectheta)=-1.`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    OBJECTIVE RD SHARMA|Exercise Section I - Solved Mcqs|92 Videos

  • DIFFERENTIATION

    OBJECTIVE RD SHARMA|Exercise Exercise|60 Videos

  • DIFFERENTIALS, ERRORS AND APPROXIMATIONS

    OBJECTIVE RD SHARMA|Exercise Exercise|17 Videos

  • ELLIPSE

    OBJECTIVE RD SHARMA|Exercise Chapter Test|30 Videos

Similar Questions

Explore conceptually related problems

if f(x)=det[[sec theta,tan^(2)theta,1theta sec x,tan x,x1,tan x-tan theta,0]] then

If f(theta)=|{:(1,tantheta,1),(-tantheta,1,tantheta),(-1,-tantheta,1):}| then the set {f(theta):0lt=thetalt(pi)/(2)} is

If f(theta) = |(1,tan theta,1),(- tan theta,1,tan theta),(-1,-tan theta,1)|, " then the set " {f(theta ) : 0 le theta le (pi)/(2)} is

int(sectheta)/(sec theta+tantheta)d theta=

Simplify tan theta [(sectheta,tantheta),(tantheta,-sectheta)]+sectheta[(-tantheta,-sectheta),(-sectheta,tantheta)]

If (sectheta + tan theta)/(sectheta-tantheta) = 5/3 , then sin theta is eqaul to :

(i) (1)/(sectheta-"tan"theta)=(1+"sin"theta)/(costheta)=sectheta+"tan"theta (ii) (1)/(sectheta+"tan"theta)=(1-"sin"theta)/(costheta)=sectheta-"tan"theta

If f(x)=(2x)/(1+x^2)\ , show that f(tantheta)=sin2theta)

OBJECTIVE RD SHARMA-DIFFERENTIATION-Chapter Test
  1. If f(x)=|{:(sectheta," "tan^(2)theta,1),(thetasecx," "tanx,x),(" "1,t...

    Text Solution

    |

  2. If f(x)=log(e)[log(e)x], then what is f' (e) equal to?

    Text Solution

    |

  3. If e^y+xy=e then the value of (d^2y)/(dx^2) for x=0 is

    Text Solution

    |

  4. sqrt(x+y)+sqrt(y-x)=c , then (d^2y)/(dx^2) equals

    Text Solution

    |

  5. If a x^2+2h x y+b y^2=1,t h e n(d^(2y))/(dx^2) is (h^2-a b)/((h x+b y)...

    Text Solution

    |

  6. If f(x)=sin{(pi)/(2)[x]-x^(5)},1ltxlt2 and [.] denotes the greatest in...

    Text Solution

    |

  7. If f(x) is a polynomial of degree n(gt2) and f(x)=f(alpha-x), (where ...

    Text Solution

    |

  8. If y=sin(log(e)x), then x^(2)(d^(2)y)/(dx^(2))+x(dy)/(dx) is equal to

    Text Solution

    |

  9. If f(x)=(1-x)^(n), then the value of f(0)+f'(0)+(f''(0))/(2!)+...+(f...

    Text Solution

    |

  10. xsqrt(1+y)+ysqrt(1+x)=0 then (dy)/(dx)=

    Text Solution

    |

  11. If 8f(x)+6f(1/x)=x+5 and y=x^2(f(x), then (dy)/(dx) at x=-1 is equal t...

    Text Solution

    |

  12. If y=sin^(-1){(5x+12 sqrt(1-x^(2)))/(13)}, find (dy)/(dx).

    Text Solution

    |

  13. If f(x)=cos^(-1){(1-(log(e)x)^(2))/(1+(log(e)x)^(2))}, then f'( e )

    Text Solution

    |

  14. y=sin^(-1)[sqrt(x-a x)-sqrt(a-a x)]

    Text Solution

    |

  15. Let f(x)=(x^3+2)^(30) If f^n (x) is a polynomial of degree 20 where f^...

    Text Solution

    |

  16. If f(x)=cos^(2)x+cos^(2)(x+(pi)/(3))+sinxsin(x+(pi)/(3)) and g((5)/(4)...

    Text Solution

    |

  17. If f(x)=10cosx+(13+2x)sinx then f'(x)+f(x)=

    Text Solution

    |

  18. If a real valued function f(x) satisfies the equation f(x +y)=f(x)+f (...

    Text Solution

    |

  19. If f(x)=log{(u(x))/(v(x))},\ u(1)=v(1) and u^(prime)(1)=v^(prime)(1)=2...

    Text Solution

    |

  20. If f'(x)=arc tan((x^(x)-x^(-x))/(2)), then f'(1) is equal to

    Text Solution

    |

  21. Let f(x)=2^(2x-1)" and "g(x)=-2^(x)+2xlog2. Then the set of points sat...

    Text Solution

    |