Why is there an issue with tan^2x+3=0

Question

Why is there an issue with tan^2x+3=0

Answer 1

To spot the error here, we only need to make one small manipulation. Subtracting 3 from either side of the equation, we get the equation

tan²(x) = -3

tan(x) is a real valued function (at least in this case), and if we square a real number, we always get a positive number result. Here, our result is -3, and there's no real solution to the equation x² = -3, so this would not be a valid equation if x is a real number.

Answer 2

Do you mean tan(2x)+3=0 or tan²(x)+3=0

tan²(x)+3=0 means tan²(x)=-3, which is not possible because the square root of -3 is imaginary.

for tan(2x) + 3 = 0

tan(2x) = -3

Use a calculator, tan^-1(-3)= -71.56

So we solve 2x=-71.56

That's one solution. Remember tan(x) is periodic; its period is pi. Try to figure all of the solutions based on this hint.