How do you solve Cos(x)/Sinx=2Cos(x)

Thank CPhill for the correction and the detailed description of the correct solution.
I was a bit frivolous with the division by cos (x).
That will not happen to me.
Greeting asinus: - )

Hello Guest!

How do you solve cos(x) / sin(x)=2cos(x)

cos(x) / sin(x) = 2 cos(x)                    [ / cos(x)

1 / sin(x) = 2                                      [ reciprocal

sin(x) = 0.5

x = arcsin(0.5)

x = 30°  90°   150°

Put to the test:

cos(30°) / sin(30°) = 2 cos(30°) 

0.866 / 0.5 = 2 * 0.866

cos(90°) / sin(90°) = 2 cos(90°) 

0 / 1 = 2 * 0

cos(150°) / sin(150°) = 2 cos(150°) 

(-0866) / 0.5 = 2 *(-0.866)

Greeting asinus :- )

   !

We need to be careful about "dropping a solution" when solving this kind of problem.

Dividing away cos x will eliminate possible solutions........

We have

cosx / sinx = 2cosx      rearrange as

2cosx - cosx / sin x  = 0       factor out cos x

cosx ( 2  - 1/sinx) = 0

cos x ( 2 - csc x )   = 0        set both factors to 0

cos x   = 0     and this happens at   pi/2 + n * pi      where n i s an integer

2 - csc x   = 0     

2 = csc x        this is the same as .......      1/2 = sin x

And this happens at  pi/6  + n* 2pi       and at     5pi/6 + n *2pi       where n is an integer