Home
Class 12
MATHS
sec^2(tan^(-1)2)+cos e c^2(cot^(-1)3) is...

`sec^2(tan^(-1)2)+cos e c^2(cot^(-1)3)` is equal to (a)5 (b) 13 (c) 15 (d) 6

A

5

B

13

C

15

D

6

Text Solution

Verified by Experts

The correct Answer is:
C
Let `tan^(-1) 2 = alpha " or " tan alpha = 2`
and `cot^(-1) 3 = beta " or " cot beta = 3`
`sec^(2) (tan^(-1) 2) + cosec^(2) (cot^(-1) 3)`
`= sec^(2) alpha + cosec^(2) beta`
`= 1 + tan^(2) alpha + 1 + cot^(2) beta`
`= 2 + (2)^(2) + (3)^(2) = 15`
Promotional Banner

Topper's Solved these Questions

  • INTRODUCTION TO VECTORS

    CENGAGE|Exercise JEE Previous Year|20 Videos

  • JEE 2019

    CENGAGE|Exercise Chapter 10|9 Videos

Similar Questions

Explore conceptually related problems

int e^(tan^-1x)(1+x+x^2) d(cot^-1x) is equal to

The value of 2tan^(-1)(cos e ctan^(-1)x-tancot^(-1)x) is equal to (a) cot^(-1)x (b) cot^(-1)1/x (c) tan^(-1)x (d) none of these

If y="sec"(tan^(-1)x), then (dy)/(dx) at x=1 is equal to: 1/(sqrt(2)) (b) 1/2 (c) 1 (d) sqrt(2)

If y="sec"(tan^(-1)x), then (dy)/(dx) at x=1 is equal to: 1/(sqrt(2)) (b) 1/2 (c) 1 (d) sqrt(2)

If sintheta_1sintheta_2-costheta_1costheta_2+1=0, then the value of tan((theta_1)/2)cot((theta_2)/2) is equal to (a) -1 (b) 1 (c) 2 (d) -2

tan(pi/4+1/2cos^(-1)x)+tan(pi/4-1/2cos^(-1)x),x!=0, is equal to x (b) 2x (c) 2/x (d) none of these

("lim")_(xvecoo)"{"x+5")"tan^(-1)(x+5)-(x+1)tan^(-1)(x+1)} is equal to (a) pi (b) 2pi (c) pi/2 (d) none of these

lim_(x->oo) (e^(1/x^2)-1)/(2tan^-1(x^2)-pi) is equal to (a) 1 (b) -1 (c) 1/2 (d) -1/2

lim_(x->oo)cot^(-1)(x^(-a)log_a x)/(sec^(-1)(a^xlog_x a)),(a >1) is equal to (a) 2 (b) 1 (c) (log)_a2 (d) 0

If 5tantheta=4, then (5sintheta-3costheta)/(5sintheta+2costheta) is equal to 0 (b) 1 (c) 1/6 (d) 6

CENGAGE-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. If cot^(-1)n/pi>pi/6,n in N , then the maximum value of n is 6 (b) ...

    Text Solution

    |

  2. If cosec^(-1) (cosec x) and cosec (cosec^(-1) x) are equal function th...

    Text Solution

    |

  3. sec^2(tan^(-1)2)+cos e c^2(cot^(-1)3) is equal to (a)5 (b) 13 (c) 15...

    Text Solution

    |

  4. The maximum value of f(x)=tan^(-1)(((sqrt(12)-2)x^2)/(x^4+2x^2+3)) is...

    Text Solution

    |

  5. For the equation cos^(-1)x+cos^(-1)2x+pi=0 , the number of real soluti...

    Text Solution

    |

  6. The number of real solution of the equation tan^(-1) sqrt(x^(2) - 3x +...

    Text Solution

    |

  7. If sin^(-1)(x-1)+cos^(-1)(x-3)+tan^(-1)(x/(2-x^2))=cos^(-1)k+pi, then ...

    Text Solution

    |

  8. The number of real solution of the equation sqrt(1+cos2x)=sqrt2 sin^(-...

    Text Solution

    |

  9. Find the set of value of x for which the equation cos^(-1) x + cos^(-1...

    Text Solution

    |

  10. Range of f(x)=sin^(-1)x+tan^(-1)x+sec^(-1)x is (pi/4,(3pi)/4) (b) [pi...

    Text Solution

    |

  11. The value of lim(|x| rarr oo) cos (tan^(-1) (sin (tan^(-1) x))) is equ...

    Text Solution

    |

  12. Find the range of tan^(-1)((2x)/(1+x^2))

    Text Solution

    |

  13. Complete solution set of (cot^(-1)x)+2(tan^(-1)x)=0, where [] denotes ...

    Text Solution

    |

  14. The number of integral values of k for which the equation sin^(-1)x+ta...

    Text Solution

    |

  15. The range of value of p for which the equation sincos^(-1)("cos"(tan^(...

    Text Solution

    |

  16. The sum of the solution of the equation 2sin^(-1)sqrt(x^2+x+1)+cos^(-1...

    Text Solution

    |

  17. Complete solution set of tan^2(sin^(-1)x)>1 is (a)(-1,-1/(sqrt(2)))uu...

    Text Solution

    |

  18. If sin^(-1)x=2sin^(-1)alpha has a solution, then

    Text Solution

    |

  19. The number of solution of equation sin^(-1)x+nsin^(-1)(1-x)=(mpi)/2,w ...

    Text Solution

    |

  20. If |cos^(-1)((1-x^2)/(1+x^2))|<pi/3,t h e n

    Text Solution

    |