Home
Class 12
MATHS
If tan theta1,tantheta2,tan theta3,tan t...

If `tan theta_1,tantheta_2,tan theta_3,tan theta_4` are the roots of the equation `x^4-x^3sin2beta+x^2cos2beta-xcosbeta-sinbeta=0` then prove that `tan(theta_1+theta_2+theta_3+theta_4)=cot beta `

Text Solution

Verified by Experts

The correct Answer is:
`cot beta`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS|Exercise Exercise For Session 1|10 Videos

  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS|Exercise Exercise For Session 2|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 tan theta_(1),tan theta_(2),tan theta_(3),tan theta_(4) are the roots of the equation x^(4)-x^(3)sin2 beta+x^(2)cos2 beta-x cos beta-sin beta=0 then prove that tan(theta_(1)+theta_(2)+theta_(3)+theta_(4))=cot beta

tantheta+tan2theta=tan3theta

(tan5 theta+tan3 theta)/(tan5 theta-tan3 theta)=4cos2 theta cos4 theta

If tan 2 theta.tan 4 theta =1 , then the value of 3 theta is

If: tantheta + tan 2theta + tan 3theta = tan theta.tan2theta.tan 3theta , then: theta =

Solve tan theta + tan 2 theta + tan theta * tan 2 theta * tan 3 theta=1

Prove that (tan5 theta+tan3 theta)/(tan5 theta-tan3 theta)=4cos2 theta cos4 theta

If tan2theta.tan4theta=1 , find sin2theta+cos4theta=?

If 1+sin^(2)theta=3sin theta cos theta, then prove that tan theta=1 ot tan theta=(1)/(2)

f theta_(1),theta_(2),theta_(3),theta_(4),theta_(5)in(0,(pi)/(2)), satisfying tan theta_(1)tan theta_(2)tan theta_(3)tan theta_(4)tan theta_(5)=1 then maximum_(2 value of )theta_(3)tan theta_(4)cos theta_(5) is cos theta_(1)cos theta_(2)cos theta_(3)cos theta_(4)cos theta_(5) is

ARIHANT MATHS-TRIGONOMETRIC FUNCTIONS AND IDENTITIES-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If tan theta1,tantheta2,tan theta3,tan theta4 are the roots of the equ...

    Text Solution

    |

  2. If alpha and beta are non-zero real number such that 2(cos beta-cos al...

    Text Solution

    |

  3. Let -1/6 < theta < -pi/12 Suppose alpha1 and beta1, are the root...

    Text Solution

    |

  4. The value of sum(k=1)^(13) (1)/(sin(pi/4 + ((k-1)pi)/(6))sin(pi/4 + (k...

    Text Solution

    |

  5. Let f : (-1, 1) -> R be such that f(cos4theta) = 2/(2-sec^2theta for t...

    Text Solution

    |

  6. The number of all possible values of theta, where 0 lt theta lt pi, f...

    Text Solution

    |

  7. For 0 lt theta lt pi/2, the solution (s) of sum(m=1)^(6) cosec (the...

    Text Solution

    |

  8. If sin^ 4 x/2+cos^4 x/3 =1/5 then

    Text Solution

    |

  9. Let theta in (0,pi/4) and t1=(tan theta)^(tan theta), t2=(tan theta)6(...

    Text Solution

    |

  10. cos(alpha-beta)=1a n dcos(alpha+beta)=l/e , where alpha,betamu in [-pi...

    Text Solution

    |

  11. If 5(tan^2x - cos^2x)=2cos 2x + 9, then the value of cos4x is

    Text Solution

    |

  12. Let fk(x) = 1/k(sin^k x + cos^k x) where x in RR and k gt= 1. Then f4(...

    Text Solution

    |

  13. The expression (tanA)/(1-cotA)+(cotA)/(1-tanA) can be written as (1) s...

    Text Solution

    |

  14. If a Delta PQR " if" 3 sin P + 4 cos Q = 6 and 4 sin Q + 3 cos P =1 , ...

    Text Solution

    |

  15. If A = sin^2x + cos^4 x, then for all real x :

    Text Solution

    |

  16. Let cos (alpha+beta) = 4/5 and sin(alpha-beta)=5/13 where 0<= alpha,...

    Text Solution

    |

  17. If cosalpha+cosbeta+cosgamma=0=sinalpha+sinbeta+singamma, then which...

    Text Solution

    |

  18. A triangular park is enclosed on two sides by a fence and on the third...

    Text Solution

    |

  19. If 0 lt x lt pi and cos x + sin x = 1/2, then tan x is

    Text Solution

    |

  20. In Delta PQR , /R=pi/4, tan(P/3), tan(Q/3) are the roots of the equati...

    Text Solution

    |