Home
Class 12
MATHS
If tantheta=sqrt(n), where n in N ,geq2...

If `tantheta=sqrt(n),` where `n in N ,geq2,t h e nsec2theta` is always a rational number (b) an irrational number a positive integer (d) a negative integer

A

a rational number

B

an irrational number

C

a positive integer

D

a negative integer.

Text Solution

Verified by Experts

The correct Answer is:
A
`tan theta=sqrt(n)`
`rArr cos 2theta=(1-tan^(2)theta)/(1+tan^(2)theta)=(1-n)/(1+n)` =rational
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise (Multiple)|22 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise (Comprehension)|20 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Exercise 3.10|5 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise SINGLE CORRECT ANSWER TYPE|38 Videos

  • TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS

    CENGAGE|Exercise Multiple Correct Answers Type|6 Videos

Similar Questions

Explore conceptually related problems

If tantheta=sqrt n, where n in N, >= 2, then sec2theta is always (a) a rational number (b) an irrational number (c) a positive integer (d) a negative integer

The 10 th term of (3-sqrt((17)/(4)+3sqrt(2)))^(20) is (a)a irrational number (b)a rational number (c)a positive integer (d)a negative integer

sqrt(2)backslash s backslash a/ an rational number (b) natural number irrational number (d) integer

The number log _(2)7 is (1990,2M) an integer (b) a rational number an irrational number (d) a prime number

3.27is (a) an integer (b) a rational number (c) a natural number (d) an irrational number

If a^2 = 23/25 , then a is: (a) rational (b) irrational (c) whole number (d) integers

The number 0.318564318564318564 is: a natural number (b) an integer a rational number (d) an irrational number

If n is a natural number,the sqrt(n) always a natural number always an irrational number always an irrational number somexx a natural number and somexx an irrational number

If n is a positive integer,then (sqrt(3)+1)^(2n)-(sqrt(3)-1)^(2n) is (1) an irrational number (2) an odd positive integer (3) an even positive integer (4) a a rational number other than positive integers

CENGAGE-TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS-Exercise (Single)
  1. cos e c(360^0)/7+cos e c(540^0)/7= cos e c(180^0)/7 (b) cos e c(90^0...

    Text Solution

    |

  2. If theta1a n dtheta2 are two values lying in [2,2pi] for which t a nth...

    Text Solution

    |

  3. If tantheta=sqrt(n), where n in N ,geq2,t h e nsec2theta is always a ...

    Text Solution

    |

  4. If sin2theta=cos3theta and theta is an acute angle , then sintheta is ...

    Text Solution

    |

  5. If cosx= tany, cosy= tanz and cosz= tanx, prove that sinx= siny= sinz ...

    Text Solution

    |

  6. The value of cot70^(@)+4cos70^@ is

    Text Solution

    |

  7. If sinx+cosx=sqrt7/2 where xin[0,pi/4] then tan(x/2) is equal to

    Text Solution

    |

  8. If (tan3A)/(tanA)=k(k!=1) then which of the following is not true? (co...

    Text Solution

    |

  9. If x in (pi,(3pi)/2),t h e n4cos^2(pi/4-x/2)+sqrt(4sin^4x+sin^2 2x) is...

    Text Solution

    |

  10. If cosx=(2cosy-1)/(2-cosy), where x , y in (0,pi) then tanx/2coty/2 is...

    Text Solution

    |

  11. cot16^0cot44^0+cot44^0cot76^0-cot76^0cot16^0= 1 (b) 2 (c) 3 (d) ...

    Text Solution

    |

  12. If tan x = b/a then sqrt((a+b)/(a-b)) + sqrt((a-b)/(a+b)) is equal to

    Text Solution

    |

  13. Given that (1+sqrt(1+x))tany=1+sqrt(1-x) . Then sin4y is equal to 4x ...

    Text Solution

    |

  14. If cos 2B =cos(A+C)/cos( A-C), then tanA, tanB, tanC are in

    Text Solution

    |

  15. If ("cos"(x-y))/("cos"(+y))+("cos"(z+t))/(cos(z-t))=0 , then the value...

    Text Solution

    |

  16. If tan beta=2sin alpha sin gamma co sec(alpha+gamma), then cot alpha,c...

    Text Solution

    |

  17. the value of tan9^@-tan2 7^@-tan6 3^@+tan8 1^@ is equal to

    Text Solution

    |

  18. If cos^3xsin2x=sum(r=0)^n axsin(r x),AAx in R then

    Text Solution

    |

  19. cos^6pi/9-33tan^4pi/9+27tan^2pi/9 is equal to 0 (b) sqrt(3) (c) 3 ...

    Text Solution

    |

  20. Given that a , b , c , are the side of a A B C which is right angled ...

    Text Solution

    |