Home
Class 11
MATHS
Prove that: tanA + tan(60^(@)+A) + tan(1...

Prove that: `tanA + tan(60^(@)+A) + tan(120^(@)+A)=3tan3A`

Text Solution

AI Generated Solution

To prove that \( \tan A + \tan(60^\circ + A) + \tan(120^\circ + A) = 3\tan 3A \), we will follow these steps: ### Step 1: Rewrite the left-hand side We start with the left-hand side (LHS): \[ LHS = \tan A + \tan(60^\circ + A) + \tan(120^\circ + A) \] ...
Promotional Banner

Topper's Solved these Questions

  • BASIC MATHS,LOGARITHIM, TRIGNOMETRIC RATIO AND IDENTITIES AND TRIGNOMETRIC EQUATION

    ALLEN|Exercise EXERCISE (JM)|8 Videos

Similar Questions

Explore conceptually related problems

Prove that : t a n A+tan(60^0+A)+tan(120^0+A)=3t a n3A

Prove that: t a nA+tan(60^0+A)-t a n(60^0-A)=3t a n3A

Prove that: t a nA+tan(60^0+A)-t a n(60^0-A)=3t a n3A

Prove that: tan10^(@) tan20^(@)tan70^(@)tan80^(@)=1

Prove that tan (2 tan^(-1) x ) = 2 tan (tan^(-1) x + tan^(-1) x^(3)) .

Prove that : tan 20^0 tan 40^0 tan 60^0 tan 80^0 =3

Prove that: (a) tan 20^(@)tan40^(@)tan60^(@)tan 80^(@)=3 (b) tan9^(@)-tan27^(@)-tan63^(@)+tan81^(@)=4

Prove that tan 9^(@) - tan 27^(@) -tan 63^(@) + tan 81^(@) =4

Prove that: tanA(1+sec2A)=tan2A

Prove that: tantheta.tan(60^0-theta).tan(60^0+theta)=tan3thetadot.'

ALLEN-BASIC MATHS LOGARITHIM TRIGNOMETRIC RATIO AND IDENTITIES AND TRIGNOMETRIC EQUATION -ILLUSTRATIONS
  1. Solve for x: (1.25)^(1-x) gt (0.64)^(2(1+sqrt(x))

    Text Solution

    |

  2. Show that log(4)18 is an irrational number.

    Text Solution

    |

  3. If in a right angled triangle, a and b are the lengths of sides and c ...

    Text Solution

    |

  4. If the arcs of same length in two circles subtend angles of 60^(@) and...

    Text Solution

    |

  5. If sintheta+sin^(2)theta=1, then prove that cos^(12)theta+3cos^(10)the...

    Text Solution

    |

  6. 4(sin^(6)theta+cos^(6)theta)-6(sin^(4)theta+cos^(4)theta)is equal to

    Text Solution

    |

  7. If sintheta=-1/2 and tantheta=1/sqrt(3) then theta is equal to,

    Text Solution

    |

  8. Prove that sqrt(3) " cosec "20^(@)-sec 20^(@)=4

    Text Solution

    |

  9. Prove that tan 70^(@)=cot70^(@)+2cot40^(@)

    Text Solution

    |

  10. If sin 2A=lambda sin 2B, prove that : (tan (A+B))/(tan(A-B)) = (lambda...

    Text Solution

    |

  11. (sin5theta+sin2theta-sin tehta)/(cos5theta+2cos3theta+2cos^(2)theta+co...

    Text Solution

    |

  12. Prove that: s in 12^0s in 48^0s in 54^0=1/8dot

    Text Solution

    |

  13. Prove that (2cos2A+1)/(2cos2A-1)=tan(60^0+A)tan(60^0-A)dot

    Text Solution

    |

  14. Prove that: tanA + tan(60^(@)+A) + tan(120^(@)+A)=3tan3A

    Text Solution

    |

  15. sin(671/2)^(@) + cos(671/2)^(@) is equal to A) 1/2sqrt(4+2sqrt(2)), ...

    Text Solution

    |

  16. The value of sin 78^@ - sin 66^@ - sin 42^@ + sin 6^@ is

    Text Solution

    |

  17. In a tringle ABC, sin A-cosB=cosC, then angle B, is

    Text Solution

    |

  18. If A+B+C =(3pi)/(2), then cos2A+cos2B+cos2C is equal to-

    Text Solution

    |

  19. Prove that 5costheta+3cos(theta+pi/3)+3 lies between -4a n d10.

    Text Solution

    |

  20. Find the maximum value of 1+sin(pi/4+theta) + 2cos(pi/4-theta).

    Text Solution

    |