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
- 30
- 20
- 15
- 10
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.