Home
Class 12
MATHS
If y=(1+t a n A)(1-t a n B), where A-B=p...

If `y=(1+t a n A)(1-t a n B),` where `A-B=pi/4,` then `(y+1)^(y-1)` is equal to 9 (b) 4 (c) 27 (d) 81

A

9

B

4

C

27

D

81

Text Solution

Verified by Experts

The correct Answer is:
C
`A-B=(pi)/(4)` or `tan (A-B)=tan""(pi)/(4)`
or `(tan A-tan B)/(1+tan A tan B)=1`
or `tan A-tan B-tan A tan B=1`
or `tan A-tan B -tan A tan B+1=2`
or `(1+tan A)(1-tan B)=2rARr y=2`
Hence, `(y+1)^(y+1)=(2+1)^(2+1)=(3)^(3)=27`.
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

Let C be incircle of A B Cdot If the tangents of lengths t_1,t_2a n dt_3 are drawn inside the given triangle parallel to sidese a , ba n dc , respectively, the (t_1)/a+(t_2)/b+(t_3)/c is equal to 0 (b) 1 (c) 2 (d) 3

In triangle A B C , if sinAcosB=1/4 and 3t a n A=t a n B ,t h e ncot^2A is equal to (a)2 (b) 3 (c) 4 (d) 5.

If y=a x^(n+1)+b x^(-n),t h e nx^2(d^2y)/(dx^2) is equal to n(n-1)y (b) n(n+1)y (c) n y (d) n^2y

If y=(sin^(-1)x)/(sqrt(1-x^2)),t h e n((1-x^2)dy)/(dx) is equal to (a) x+y (b) 1+x y (c) 1-x y (d) x y-2

If y=(log)_(sinx)(tanx),t h e n(((dy)/(dx)))_(pi/4)"is equal to" (a) 4/(log2) (b) -4log2 (c) (-4)/(log2) (d) none of these

If Aa n dB are symmetric matrices of the same order and X=A B+B Aa n dY=A B-B A ,t h e n(X Y)^T is equal to X Y b. Y X c. -Y X d. none of these

If ("cos"(x-y))/("cos"(x+y))+("cos"(z+t))/(cos(z-t))=0 , then the value of expression tanxtanytanztant is equal to (a) 1 (b) -1 (c) 2 (d) -2

If x^2+y^2+z^2=r^2,t h e ntan^(-1)((x y)/(z r))+tan^(-1)((y z)/(x r))+tan^(-1)((x z)/(y r)) is equal to (a) pi (b) pi/2 (c) 0 (d) none of these

The slope of the tangent to the curve y=sqrt(4-x^2) at the point where the ordinate and the abscissa are equal is -1 (b) 1 (c) 0 (d) none of these

If tanx=ntany ,n in R^+, then the maximum value of sec^2(x-y) is equal to (a) ((n+1)^2)/(2n) (b) ((n+1)^2)/n (c) ((n+1)^2)/2 (d) ((n+1)^2)/(4n)

CENGAGE-TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS-Exercise (Single)
  1. If cos28^0+sin28^0=k^3, t h e ncos17^0 is equal to (k^3)/(sqrt(2)) (b...

    Text Solution

    |

  2. Let f(theta)=cottheta/(1+cottheta) and alpha+beta=(5pi)/4 then the va...

    Text Solution

    |

  3. If y=(1+t a n A)(1-t a n B), where A-B=pi/4, then (y+1)^(y-1) is equal...

    Text Solution

    |

  4. If (sinx)/(siny)=1/2,(cosx)/(cosy)=3/2 , where x , y , in (0,pi/2), th...

    Text Solution

    |

  5. If cot^2x=cot(x-y)(x-z),t h e ncot2x is equal to (w h e r ex!=pi/4) ....

    Text Solution

    |

  6. In a A B C , if tanB :tanC=3:4:5, then the value of sinA sinB sinC is...

    Text Solution

    |

  7. find the value of sin 27^(@)-cos27^(@)?

    Text Solution

    |

  8. If costheta1 2costheta2, then tan(theta(1-theta2))/2tan(theta1+theta2)...

    Text Solution

    |

  9. Let alpha, beta" such that "pi lt alpha-beta lt 3pi." If sin "alpha+si...

    Text Solution

    |

  10. If n=pi/(4alpha), then tanalpha tan 2alpha tan 3 alpha........tan(2n-1...

    Text Solution

    |

  11. (sin3theta+sin5theta+sin7theta+sin9theta)/(cos3theta+cos5theta+cos7the...

    Text Solution

    |

  12. If x , y , z are in A.P., then (sinx-sinz)/(cosz-cosx) is equal to tan...

    Text Solution

    |

  13. If (cosx)/a=(cos(x+theta))/b=(cos(x+20))/c=(cos(x+3theta))/d then (a+c...

    Text Solution

    |

  14. If cos alpha + cos beta =0 = sin alpha + sin beta , then cos...

    Text Solution

    |

  15. Value of (3+cot80^0cot20^0)/(cot80^0+cot20^0) is equal to cot20^0 (b)...

    Text Solution

    |

  16. If tanalpha is equal to the integral solution of the inequality 4x^2-1...

    Text Solution

    |

  17. Let f(n)=2cosn xAAn in N , then f(1)f(n+1)-f(n) is equal to f(n+3) (...

    Text Solution

    |

  18. If sintheta1sintheta2-costheta1costheta2+1=0, then the value of tan((t...

    Text Solution

    |

  19. (sqrt(2)-sinalpha)/(sinalphapi-cosalphapi) is equal to sec(alpha/2-pi/...

    Text Solution

    |

  20. If x1a n dx2 are two distinct roots of the equation acosx+bsinx=c , th...

    Text Solution

    |