How do I solve: sqrt(3)tanx=
I need to use the identity tanx=sinx/cosx
Thanks
It equauls 2sinx
√3 tanx = 2sinx
√3 sinx/cosx - 2sinx = 0
sinx(√3/cosx - 2) = 0
sinx = 0
x = 0 , π, 2π ... , you didn't state a domain
or
√3/cosx = 2
cosx = √3/2
x = π/6 or 5π/6 ------ (30° or 150°)
To solve the equation sqrt(3)tan(x) = 0, we can use the identity tan(x) = sin(x)/cos(x).
First, let's rewrite the equation using the identity:
sqrt(3) * sin(x)/cos(x) = 0
Now, we can solve this equation.
Since sqrt(3) is a non-zero constant, the only way for the left side of the equation to equal zero is if sin(x) = 0.
So, we set sin(x) = 0 and solve for x:
sin(x) = 0
To find the values of x that satisfy this equation, we can look at the unit circle.
On the unit circle, the x-coordinates of the points where the sine function equals zero are 0, pi, 2pi, 3pi, and so on.
Therefore, the solutions to the equation sin(x) = 0 are x = 0, pi, 2pi, 3pi, and so on.
So, the solutions to the equation sqrt(3)tan(x) = 0 using the identity tan(x) = sin(x)/cos(x) are x = 0, pi, 2pi, 3pi, and so on.