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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