Home
Class 12
MATHS
Prove the following : tan6^@.tan42^@.tan...

Prove the following : `tan6^@.tan42^@.tan66^@.tan78^@ = 1`

Text Solution

Verified by Experts

We have tan3A
= tanAtan(60^@-A)tan(60^@+A)
Now putting `A=6^@` and `18^@`.
in (1) we have
`tan18^@=tan6^@tan54^@tan66^@......(2)
and `tan54^@`
=`tan18^@tan42^@tan78^@` ......(3)
Multiplying (2) and (3) we have
`tan18^@tan54^@`
=`tan6^@tan54^@tan66^@tan18^@tan42^@tan78^@`
or, 1=`tan6^@tan42^@tan66^@tan78^@`.
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    MBD PUBLICATION|Exercise QUESTION BANK|523 Videos

  • VECTORS

    MBD PUBLICATION|Exercise QUESTION BANK|138 Videos

Similar Questions

Explore conceptually related problems

Prove the tan10^@+tan35^@+tan10^@.tan35^@ = 1

Prove the following : (1-tan^2(45^@-A))/(1+tan^2(45^@-A)) = sin2A

Prove the following : tan4theta = (4tantheta-4tan^3theta)/(1-6tan^2theta+tan^4theta)

Solve the following: tan x + tan 4x+tan 7x =tan x tan 4x tan 7x

Solve the following: tan theta + tan 2theta = tan 3theta

Prove the following : tan37(1/2)^@=sqrt6+sqrt3-sqrt2+2

Prove the following "tan"^(-1)(2a-b)/(bsqrt(3))+"tan"^(-1)(2b-a)/(asqrt(3))=pi/(3)

Solve the following equations "tan"^(-1)1/(3)+"tan"^(-1)1/(5)+"tan"^(-1)1/(7)+"tan"^(-1)x=pi/(4)

Directions (Q. Nos. 16-25) Prove the following "cos"(2"tan"^(-1)1/(7))="sin"(4"tan"^(-1)1/(3)) .

Solve the following: tan theta + tan(theta+frac{pi}{3})+ tan(theta+frac{2pi}{3})=3

MBD PUBLICATION-TRIGONOMETRIC FUNCTIONS-QUESTION BANK
  1. Prove the following : cos10^@.cos30^@.cos50^@.cos70^@ = 3/16

    Text Solution

    |

  2. Prove the following : cos20^@.cos40^@.cos60^@.cos80^@ = 1/16

    Text Solution

    |

  3. Prove the following : tan6^@.tan42^@.tan66^@.tan78^@ = 1

    Text Solution

    |

  4. Prove the following : cot7(1/2)^@=sqrt6+sqrt3+sqrt2+2

    Text Solution

    |

  5. Prove the following : cot22(1/2)^@=sqrt2+1

    Text Solution

    |

  6. Prove the following : cot37(1/2)^@=sqrt6-sqrt3-sqrt2+2

    Text Solution

    |

  7. Prove the following : tan37(1/2)^@=sqrt6+sqrt3-sqrt2+2

    Text Solution

    |

  8. Prove the following : cos(pi/16)=1/2 sqrt(2+sqrt(2+sqrt2))

    Text Solution

    |

  9. If sin A=K sin B, prove the tan frac{1}{2}(A-B)=frac{K-1}{K+1 }tan ...

    Text Solution

    |

  10. If a cos(x+a)=b cos(x-a) show that (a+b) tan x=(a-b) cot a

    Text Solution

    |

  11. An angle theta is divided into two parts alpha, beta such that tan alp...

    Text Solution

    |

  12. If sin theta +sin phi=a,cos theta+cos phi=b, show that sinfrac{theta+...

    Text Solution

    |

  13. If a cosalpha+bsin alpha=c=a cos beta+b sin beta then prove that fra...

    Text Solution

    |

  14. Prove that (frac{cosA+cosB}{sinA-sinB})^n+(frac{sinA+sinB}{cosA-cosB})...

    Text Solution

    |

  15. If (1-e)tan^2frac{beta}{2}=(1+e)tan^2frac{alpha}{2}. prove that cosbet...

    Text Solution

    |

  16. If costheta=(cosA-cosB)/(1-cosA cdotcosB) prove that one of the value...

    Text Solution

    |

  17. If tan theta=(sinxcdot siny)/(cos x + cos y) then prove that one of ...

    Text Solution

    |

  18. If sec(phi+alpha)+sec(phi-alpha)=2secphi show that cosphi=+-sqrt2cosfr...

    Text Solution

    |

  19. If tanA+tanB=a and cotA+cotB=b then show that cot(A+B)=1/a-1/b

    Text Solution

    |

  20. If cottheta=cos(x+y)andcotphi=cos(x-y) then show that tan(theta-phi)=...

    Text Solution

    |