Question

Need help solving the following for x,
Sin(2x)-Tan(x)=0

Answer 1

Suggestion 1: There is an identity for sin 2x which would be helpful here. Please look it up and use it.
Suggestion 2: the tangent function can be re-written in terms of the sine and cosine functions.

Answer 2

I know you can use the double-angle identity for sine. So it would be 2Sin(x)Cos(x)-SIn(x)/Cos(x). But were do i go from there.

Answer 3

@mathmale

Answer 4

mult both sides by cos(x). but remember, \(x = \Large\frac{\pi}{2} \normalsize{+k\pi,\,\,k \in \mathbb{Z}}\) is not a solution (division by 0).

then see what you get and if you can solve it.

Answer 5

\[
\sin(2x) = 2\sin(x)\cos(x)
\]\[
\tan(x) = \frac{\sin(x)}{\cos(x)}
\]

Answer 6

sin2x - tanx =
2sinxcosx - sinx/cosx =
sinx(2cosx - 1/cosx) =
0

So sinx = 0, which happens when x = 0,180 or
2cosx = 1/cosx
cosx = +/-(1/root2)

Answer 7

x = 45, 135, 225, 315