Question

sq3tanx=2sinx I am having trouble breaking these down so if you could answer with the steps that would be great :) 0<=x<2pi

Answer 1

okay put sin(x) and tan(x) in one side and the other in the other side

Answer 2

tan(x)/sin(x)=2/sq(3)

Answer 3

tan(x)=sin(x)/cos(x)
so....(sin(x)/cos(x))/sin(x))=sin(x)/(cos(x)*sin(x)=1/cos(x)

Answer 4

Our initial equation:\[\sqrt{3}\tan(x)=2sinx\]
Express tan(x) in terms of sin(x) and cos(x)
\[\sqrt{3}\frac{ \sin(x) }{ \cos(x) } = 2\sin(x)\]
Divide by sin(x) (Note: this is potentially 0 so we must remember a solution is sin(x)=0 later on!)
\[\sqrt{3}\frac{ 1 }{ \cos(x) } = 2\]
Rearrange to get an equation for cos(x):
\[\cos(x)=\frac{ \sqrt{3} }{ 2 }\]

Our solutions are: x=0, x=pi/6, x=11pi/6

Answer 5

so cos(x)=sq(3)/2

Answer 6

I thank all of you :)