# 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.