Question

tan^2 x + sqr3 tanx = 0 solve please

Answer 1

tan x = sin x / cos x
In each quadrant, tan takes on all the values of one sign with magnitudes ranging from 0 to ∞. It is negative in [π/2, π] and in [3π/2, 2π].

Knowing that tan π/6 = tan 30º = (sin π/6)/(cos π/6) = (1/2)(√3/2) = 1/√3,
and that tan(x+π/2) = -1/tan x, you can see that
tan(2π/3) = tan(π/6 + π/2) = -√3, and that
tan(x+π) = tan(x+π/2+π/2) = -1/tan(x+π/2) = tan x, so
tan(5π/3) = tan(2π/3) = -√3
so
x = 2π/3, 5π/3, if you're in the [0 to 2π] full circle;
x = 2π/3, -π/3, if you're in the [-π to π] full circle

Lemme know if this helps, if you need more help @~Chance~

Answer 2

You can just factor this. You would solve it the same way you sould solve
\[x ^{2}+\sqrt{3}x \implies x(x+\sqrt{3})\]

Just do that, but factor out a tan(x) instead. Then you set both factors equal to 0 and solve for each.

Answer 3

thanks both of you

Answer 4

Best responce me please?