Home
Class 12
MATHS
(1-tanalphatanbeta)^2+(tanalpha+tanbeta)...

`(1-tanalphatanbeta)^2+(tanalpha+tanbeta)^2=`

A

`tan^2alphatan^2beta`

B

`sec^2alphasec^2beta`

C

`tan^2alphacot^2beta`

D

`sec^2alphacos^2beta`

Text Solution

Verified by Experts

The correct Answer is:
B
`(1+tanalphatanbeta)^2+(tanalpha-tanbeta)^2`
`=1+2tanalphatanbeta+tan^2alphatan^2beta+tan^2alpha+tan^2beta-2tanlphatanbeta`
`=1tan^2alphatan^2beta+tan^2alpha+tan^2beta`
`+(1+tan^2alpha)(1+tan^2beta)`
`=sec^2alphasec^2beta`
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

If sin alpha=(12)/(13), cos beta =4/5 and alpha, beta are two acute angles, then Value of (tanalpha-tan beta)/(1+tanalpha tan beta) is

By geometrical interpretation, prove that tan(alpha+beta)=(tanalpha+tanbeta)/(1-tanalphatanbeta) .

If tantheta=(tanalpha+tanbeta)/(1+tanalphatanbeta) ,then show that sin2theta=(sin2alpha+sin2beta)/(1+sin2alphasin2beta)

If tan(alpha-beta)=(sin2beta,)/(3-cos2beta) then (a) tanalpha=2tanbeta (b) tanbeta=2tanalpha (c) 2tanalpha=3tanbeta (d) 3tanalpha=2tanbeta

If alpha!=beta and atanalpha+b tanbeta=(a+b)tan((alpha+beta)/2) ,then show that (cosalpha)/(cosbeta)=a/b

Let alpha,betaa n dgamma be some angles in the first quadrant satisfying tan(alpha+beta)=(15)/8a n dcos e cgamma=(17)/8, then which of the following hold(s) good? (a) alpha+beta+gamma=pi (b) cotalpha+cotbeta+cotgamma=cotalphacotbetacotgamma (c) tanalpha+tanbeta+tangamma=tanalphatanbetatangamma (d) tanalphatanbeta+tanbetatangamma+tangammatanalpha=1

Show that tanalphatanbeta=tan^2gamma when tan(alpha-beta)/tanalpha+sin^2gamma/sin^2alpha=1

If tanbeta=(tanalpha+tangamma)/(1+tanalphatangamma)dot prove that sin2beta=(sin2alpha+sin2gamma)/(1+sin2alphasin2gamma) .

If sectheta=secalphassecbeta+tanalphatanbeta ,show that tantheta=+-(secalphatanbeta+tanalphasecbeta)

If 3sinbeta=sin(2alpha+beta) then tan(alpha+beta)-2tanalpha is (a)independent of alpha (b)independent of beta (c)dependent of both alpha and beta (d)independent of both alpha and beta

CENGAGE PUBLICATION-TRIGONOMETRIC FUNCTIONS -Exercises
  1. 3(sintheta-costheta)^4+6(sintheta+costheta)^2+4(sin^6theta+cos^6theta)...

    Text Solution

    |

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

    Text Solution

    |

  3. (1-tanalphatanbeta)^2+(tanalpha+tanbeta)^2=

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  8. Which of the following is correct?

    Text Solution

    |

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

    Text Solution

    |

  10. If sin^2theta=(x^2+y^2=1)/(2x) , then x must be -3 (b) -2 (c) 1 (d)...

    Text Solution

    |

  11. sec^2theta=4xy/(x+y)^2 is true if and only if

    Text Solution

    |

  12. If sinx+siny+sinz=3," then "cosx+cosy+cosz is equal to

    Text Solution

    |

  13. If sinx+sin y+sinz+sinw=-4, then the value of sin^(400)x+sin^(300)y+si...

    Text Solution

    |

  14. Prove that, SinA/(1-cosA) =CosecA+cotA

    Text Solution

    |

  15. If 1+sinx+sin^2x+sin^3x+oo is equal to 4+2sqrt(3),0<x<pi, then x is eq...

    Text Solution

    |

  16. The value of expression (2sin^2 91^0-1)(2sin^2 92^0-1)......(2sin^2 18...

    Text Solution

    |

  17. If sinA=sin^2Ba n d2cos^2A=3cos^2B then the triangle A B C is right an...

    Text Solution

    |

  18. If sintheta+costheta=1/5and 0lethetaltpi" then "cottheta is

    Text Solution

    |

  19. If π<α<(3π)/2 then sqrt((1-cosalpha)/(1+cosalpha))+sqrt((1+cosalpha)/...

    Text Solution

    |

  20. If 0 < alpha < pi/ 6 then alpha(cosec alpha) is

    Text Solution

    |