Home
Class 12
MATHS
If tan theta tan phi=sqrt((a-b)/(a+b)), ...

If `tan theta tan phi=sqrt((a-b)/(a+b))`, prove that
`a-bcos 2theta)(a-b cos 2phi)` is independent of `theta` and `phi`.

Text Solution

Verified by Experts

The correct Answer is:
So, `(a-b cos 2 theta) (a-b cos 2 phi)=a^(2)-b^(2)`, which is independent of `theta` and `phi`.
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.tan phi = sqrt ((a -b)/(a +b)), then (a -b cos 2 theta)(a -b cos 2 phi) is

tan theta.tan phi=sqrt((a-b)/(a+b)), then (a-b cos2 theta)(a-b cos2 phi)=

If tan theta* tan phi = sqrt((x-y)/(x+y)) prove that (x - y cos 2theta)(x - y cos 2phi) = x^(2) – y^(2)

If tan(theta)/(2)=sqrt((a-b)/(a+b))tan(phi)/(2), prove that cos theta=(a cos phi+b)/(a+b cos phi)

If 3 tan theta tan phi=1 , then prove that 2 cos (theta+varphi)=cos (theta-varphi) .

If 3tan theta tan phi=1, then prove that 2cos(theta+phi)+cos(theta-phi)=0

If tan theta = 1 and sin phi = (1)/( sqrt(2)) , then the value of cos (theta + phi) is

If 3tan theta tan phi=1. Prove that 2cos(theta+phi)=cos(theta-phi)

If sqrt(a + b) tan = theta/2 = sqrt(a -b) tan phi/2 then prove that a + b cos phi = (a cos phi+ b) sec theta .

If 3 tan theta tan phi=1, then (cos (theta-phi))/(cos (theta+phi)) is

ARIHANT MATHS-TRIGONOMETRIC FUNCTIONS AND IDENTITIES-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If tan theta tan phi=sqrt((a-b)/(a+b)), prove that a-bcos 2theta)(a-...

    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

    |