Home
Class 12
MATHS
If cosx+secx=2," then "cos^nx+sec^nx is ...

If `cosx+secx=2," then "cos^nx+sec^nx` is equal to

A

2

B

`2^n`

C

`2^(n-1)`

D

`2^(n-2)`

Text Solution

Verified by Experts

The correct Answer is:
A
`sinx+cosecx=2`
`or (sinx-1)^2=0`
`or sinx=1`
`rArr sin^nx+cosec^nx=1+1=2`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|17 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Linked Comprehension Type|11 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Concept Application Exercises 2.14|1 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE PUBLICATION|Exercise Archives (Numerical value type)|4 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|2 Videos

Similar Questions

Explore conceptually related problems

int(secx."cosec"x)/(2cotx-secx"cosec x")dx is equal to

inte^(tanx)(secx-sinx)dx"is equal to"

if cosx+secx=(-2) then for a positive integer n cos^nx+sec^nx is

int(secx)/(sqrt(cos2x)) dx is equal to

3(sinx-cosx)^4+6(sinx+cosx)^2+4(sin^6x+cos^6x) is equal to

If sec(theta+alpha)+sec(theta-alpha)=2/costheta . then cos^2theta is equal to

If f(x)=cosx-cos^(2)x+cos^(3)x-…oo , then the value of int f(x) dx is equal to -

int sqrt((cosx-cos^3x)/(1-cos^3x))dx is equal to

lim _(xto0) (1-cos mx)/(1-cos nx) is equal to-

If 2sec^2A-sec^4A-2cos e c^2A+cos e c^4A=(15)/4,then tan A is equal

CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS -Exercises
  1. If tantheta =3," then " (sintheta-costheta)/(sintheta+costheta) is equ...

    Text Solution

    |

  2. If tantheta =-4/3," then " costheta is

    Text Solution

    |

  3. If cosx+secx=2," then "cos^nx+sec^nx is equal to

    Text Solution

    |

  4. If tantheta+sintheta=mandtantheta-sintheta=n,then

    Text Solution

    |

  5. If cosectheta+cottheta=m, then the value of cosectheta is

    Text Solution

    |

  6. If (sinx)/a=(cosx)/b=(tanx)/c=k , then b c+1/(c k)+(a k)/(1+b k) is eq...

    Text Solution

    |

  7. If sec^4theta+sec^2theta=10+tan^4theta+tan^2theta", then "sin^2theta=

    Text Solution

    |

  8. If x=(2sintheta)/(1+costheta+sintheta),t h e n(1-costheta+sintheta)/(1...

    Text Solution

    |

  9. If secalpha and cosecalpha are the roots of the equation x^2-px+q=0, t...

    Text Solution

    |

  10. Which of the following is not the quadratic equation whose roots are c...

    Text Solution

    |

  11. If sinx+sin^2x=1n then the value of cos^12x+3cos^10x+3cos^8x+cos^6x-1 ...

    Text Solution

    |

  12. 3(sintheta-costheta)^4+6(sintheta+costheta)^2+4(sin^6theta+cos^6theta)...

    Text Solution

    |

  13. If secx+sec^2x=1 then the value of tan^8x-tan^4x-2tan^2x+1 will be equ...

    Text Solution

    |

  14. (1-tanalphatanbeta)^2+(tanalpha+tanbeta)^2=

    Text Solution

    |

  15. Let A0A1A2A3A4A5 be a regular hexagon inscribed in a circle of unit ra...

    Text Solution

    |

  16. A circle is drawn in a sector of a larger circle of radius r , as show...

    Text Solution

    |

  17. A right triangle has perimeter of length 7 and hypotenuse of length 3....

    Text Solution

    |

  18. Given that the side length of a rhombus is the geometric mean of the ...

    Text Solution

    |

  19. Which of the following is correct?

    Text Solution

    |

  20. The equation sin^2theta=(x^2+y^2)/(2x y),x , y!=0 is possible if

    Text Solution

    |