If tan(x+40)° tan(x+20)°tan(3x)°tan(70-x)° tan(50-x)° =1

If tan(x+40)° tan(x+20)°tan(3x)°tan(70-x)° tan(50-x)° =1, then the value of x is equal to

  1. 30
  2. 20
  3. 15
  4. 10
Anurag Mishra Professor Asked on 7th November 2015 in Maths.
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  • 1 Answer(s)

    Answer: (3) 15 

    Solution:-
    tan(x + 40)degree = cot[90 – (x + 4)]
    = cot(50 – x)degree
    = 1/tan (50 – x) degree
    As,
    tan (x – 20)degree:1/tan (70 – x)
    tan 3x,tan (70 – x): 1/tan(50 – x) = 1
    => tan 3x = 1 = tan 45 degree
    3 x = 45
    x = 45/3
    x = 15 degree

    Then, the value of x is 15.

    Hence, the  correct answer is option (3) 15.

    Anurag Mishra Professor Answered on 12th May 2016.
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