Home
Class 12
MATHS
If |tan A| lt A is acute, then (sqrt((...

If `|tan A| lt A` is acute, then
`(sqrt((1+sin2A))+sqrt((1-sin2A)))/(sqrt((1+sin2A))-sqrt((1-sin2A)))` is equal to

A

`tan A`

B

`-tan A`

C

`cot A`

D

`-cot A`

Text Solution

Verified by Experts

The correct Answer is:
C
We have, `|tanA|le 1 and|A|` is acute.
`therefore-(pi)/(4)ltAlt(pi)/(4)impliescosA gt sinA` Now,
`(sqrt(1+sin2A)+sqrt(1-sin2A))/(sqrt(a+sin2A)-sqrt(1+sin2A))` is equa to
`=(sqrt((cosA+sinA)^(2))+sqrt((cosA-sinA)^(2)))/(sqrt((cosA+sinA)^(2))-sqrt((cosA-sinA)^(2)))`
`=(|cosA+sinA|+|cosA-sinA|)/(|cosA+sinA|-|cosA-sinA|)`
`((cosA+sin)+(cosA-sinA))/((cosA+sinA)-(cosA-sinA))=cotA`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS AND IDENTITIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|13 Videos

  • TRIGONOMETRIC RATIOS AND IDENTITIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|189 Videos

  • TRIGONOMETRIC RATIOS AND IDENTITIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|60 Videos

  • TRIGONOMETRIC EQUATIONS AND INEQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|60 Videos

Similar Questions

Explore conceptually related problems

(sqrt(1+sin 2A)+sqrt(1-sin 2A) )/(sqrt(1 + sin 2A)-sqrt(1-sin2A)) If |tan A| < 1 , and | A I

cot^(-1)[(sqrt(1+sin x)+sqrt(1-sin x))/(sqrt(1+sin x)-sqrt(1-sin x))]=

dy/dx=(sqrt((1-sin2x)/(1+sin2x))) is equal to, 0ltxltpi/2

(sin^(-1)x)/(sqrt(1-x^(2))

If -pi lt theta lt -(pi)/(2)," then " |sqrt((1-sin theta)/(1+sintheta))+sqrt((1+sin theta)/(1-sin theta))| is equal to :

f(x)=sqrt(1-sin^(2)x)+sqrt(1+tan^(2)x) then

The value of sin^(-1)[xsqrt(1-x)-sqrt(x)sqrt(1-x^2)] is equal to

Prove that cot^(-1) ((sqrt(1 + sin x) + sqrt(1 - sin x))/(sqrt(1 + sin x) - sqrt(1 - sin x))) = (x)/(2), x in (0, (pi)/(4))

Biggest among (sin1+cos1),(sqrt(sin1))+sqrt(cos1)),sqrt(1+sin2)and 1, is

If theta lies in the second quadrant. Then the value of sqrt((1-sin theta)/(1+sin theta))+sqrt((1+sin theta)/(1-sin theta)) is equal to :

OBJECTIVE RD SHARMA ENGLISH-TRIGONOMETRIC RATIOS AND IDENTITIES-Section I - Solved Mcqs
  1. If 0lt thetalt(pi)/(2')and if(y+1)/(1-y)=sqrt((1+sintheta)/(1-sintheta...

    Text Solution

    |

  2. The set of all possible values of alpha in [-pi,pi] such that sqrt((1...

    Text Solution

    |

  3. If |tan A| lt A is acute, then (sqrt((1+sin2A))+sqrt((1-sin2A)))/(sq...

    Text Solution

    |

  4. sec^(2)theta==(4ab)/((a+b)^(2)), where a, b inR is true if and olny if

    Text Solution

    |

  5. Which one is true ?

    Text Solution

    |

  6. If 10sin^4 alpha+15 cos^4 alpha=6, then find the value of 27 cosec^6 a...

    Text Solution

    |

  7. Let cos(alpha + beta) = 4//5 and let sin ( alpha - beta)= 5//13, wher...

    Text Solution

    |

  8. If alpha=sin x cos^(3) x and beta=cos x sin^(3) x, then :

    Text Solution

    |

  9. The expression (tan A)/(1-cotA)+(cot A)/(1-tan A) can be written as

    Text Solution

    |

  10. Let P={theta:sintheta-costheta=sqrt2costheta}and Q={theta: sintheta+co...

    Text Solution

    |

  11. If x cos alpha+ y sin alpha= x cos beta + y sin beta=2a(0 lt alpha, be...

    Text Solution

    |

  12. If sinx+cosecx=2, then find the value of sin^(10)x+cosec^(10)x.

    Text Solution

    |

  13. The value of sin^(8)theta+cos^(8)theta+sin^(6)theta cos^(2)theta+3sin^...

    Text Solution

    |

  14. Let F(k)(x)=1/k (sin^(k)x+cos^(k)x), where x in R and k ge 1, then fin...

    Text Solution

    |

  15. If sin(theta+alpha)=a,cos^(2)(theta+beta)=b, then sin(alpha-beta)=

    Text Solution

    |

  16. Q. Let n be an add integer if sin ntheta = sum(r=0)^n(br)sin^rtheta, f...

    Text Solution

    |

  17. Which of the following number(s) is/are rational? sin15^0 (b) cos15^0...

    Text Solution

    |

  18. Let (3pi)/4 < theta < pi and sqrt(2 cot theta+1/sin^2 theta) = k - cot...

    Text Solution

    |

  19. The value of overset(13)underset(k=1)(sum) (1)/(sin((pi)/(4) + ((k-1)p...

    Text Solution

    |

  20. If A > 0, B > 0 and A+B=pi/6, then the minimum value of tan A + tan B ...

    Text Solution

    |