Home
Class 12
MATHS
If alpha,beta,gamma are acute angles and...

If `alpha,beta,gamma` are acute angles and `costheta=sinbeta//sinalpha,cosvarphi=singammasinalphaa n dcos(theta-varphi)=sinbetasingamma` , then the value of `tan^2alpha-tan^2beta-tan^2gamma` is equal to `-1` (b) `0` (c) `1` (d) 2

A

-1

B

0

C

1

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|21 Videos

  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|11 Videos

  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS|Exercise Exercise For Session 11|10 Videos

  • TRIGONOMETRIC EQUATIONS AND INEQUATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos

  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|9 Videos

Similar Questions

Explore conceptually related problems

If alpha,beta,gamma are direction - angles of a line prove that cos2 alpha+cos2beta+cos2gamma=-1

If 2 sin alphacos beta sin gamma=sinbeta sin(alpha+gamma),then tan alpha,tan beta and tan gamma are in

If a tanalpha+sqrt(a^2-1)tanbeta+sqrt(a^2+1)tangamma=2a where a is a constant and alpha,beta and gamma are variable angles. Then the least value of tan^2alpha+tan^2beta+tan^2gamma is equal to

If cos alpha , cos beta, cos gamma are the direction-cosines of a line, then the value of sin^2alpha + sin^2 beta + sin^2gamma =

If a line makes anles alpha, beta, gamma with the coordinate axes, porve that sin^2alpha+sin^2beta+sin^2gamma=2

If [(0,2beta,gamma),(alpha,beta,-gamma),(alpha,-beta,gamma)] is orthogonal, then find the value of 2alpha^(2)+6beta^(2)+3gamma^(2).

lf cos^2 alpha -sin^2 alpha = tan^2 beta , then show that tan^2 alpha = cos^2 beta-sin^2 beta .

If alpha,beta,gamma are real numbers, then without expanding at any stage, show that |1cos(beta-alpha)"cos"(gamma-alpha)"cos"(alpha-beta)1"cos"(gamma-beta)"cos"(alpha-gamma)"cos"(beta-gamma)1|=0

If alpha+beta=pi/2a n dbeta+gamma=alpha, then tanalpha equals

If a line makes angles alpha,beta,gamma respectively with positive directions of the coordinate axes, then the value of cos^(2)alpha+cos^(2)beta+cos^(2)gamma=1 .

ARIHANT MATHS-TRIGONOMETRIC FUNCTIONS AND IDENTITIES-Exercise (Single Option Correct Type Questions)
  1. If 4nalpha =pi then cot alpha cot 2 alpha cot 3alpha ...cot (2n-1)alph...

    Text Solution

    |

  2. In DeltaABC, if (Sin A + SinB + SinC) (SinA + SinB - SinC) = 3SinA Sin...

    Text Solution

    |

  3. If alpha,beta,gamma are acute angles and costheta=sinbeta//sinalpha,co...

    Text Solution

    |

  4. If t a nbeta=(n sinalphacosalpha)/(1-n sin^2alpha) , show that tan(alp...

    Text Solution

    |

  5. If (cos theta)/(a)=(sintheta)/(b), then (a)/(sec 2 theta)+(b)/(cosec 2...

    Text Solution

    |

  6. The graph of the function y = cos x cos (x+2) - cos^(2)(x+1) is

    Text Solution

    |

  7. If f (theta) = |sin theta| + |cos theta|, theta in R, then

    Text Solution

    |

  8. If P=cos(cos x)+sin (cos x), then the least and greatest value of P re...

    Text Solution

    |

  9. If u(n)=sin(n theta) sec^(n) theta, v(n)=cos(n theta) sec^(n) theta ,...

    Text Solution

    |

  10. If A=sin^(8) theta + cos^(14) theta, then for all values of theta,

    Text Solution

    |

  11. Find the value of the expression 3[sin^(4)((3pi)/(2)-alpha)+sin^(4)(...

    Text Solution

    |

  12. The maximum value of the function f(x)=sin(x+pi/6)+cos(x+pi/6) in the ...

    Text Solution

    |

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

    Text Solution

    |

  14. The minimum value of the expression sinalpha+sin beta+sin gamma, wher...

    Text Solution

    |

  15. If cos x-sin alpha cot beta sin x=cos alpha, then the value of tan (x/...

    Text Solution

    |

  16. If cos^4 theta sec^2 alpha,1/2 and sin^4 theta cosec^2 alpha are in ...

    Text Solution

    |

  17. The maximum value of (cosalpha(1))(cos alpha(2))...(cosalpha(n)), un...

    Text Solution

    |

  18. Find the set of values of x , which satisfy sin x * cos^(3) x gt cos *...

    Text Solution

    |

  19. If u=sqrt(a^2 cos^2 theta + b^2sin^2theta)+sqrt(a^2 sin^2 theta + b^2 ...

    Text Solution

    |

  20. For a positive integer n , let fn(theta)=(tantheta//2)(1+sectheta)(1+s...

    Text Solution

    |