Solving tan²x = 2tan(x)sin(x)

[TbbZz]

Homework Statement

tan^2x = 2tanx*sinx

Homework Equations

N/A

The Attempt at a Solution

tan^2x = 2tanx*sinx

(tan^2x)/tanx = (2tanx*sinx)/tanx

tanx = 2sinx

sinx/cosx = 2sinx

cosx = 1/2

x = $$pi$$/3

$$\alpha$$ = $$pi$$/3 and 5$$pi$$/3

Not sure what I'm doing wrong.

The answer is $$pi$$/3 and 5$$pi$$/3 and 0, and $$pi$$

Thanks for the assistance, I greatly appreciate it.

 

[rock.freak667]

Do not simply just divide by tanx
Bring 2tanx*sinx onto the other side and then factor out the tanx

Dividing by tanx implies that tanx is never equal to zero. Which it can be in this case.

 

[HallsofIvy]

Homework Statement

tan^2x = 2tanx*sinx

Homework Equations

N/A

The Attempt at a Solution

tan^2x = 2tanx*sinx

(tan^2x)/tanx = (2tanx*sinx)/tanx

Either tan²(x)/tan x= 2 tan(x) sin(x)/tan(x) or tan(x)= 0.

tanx = 2sinx

sinx/cosx = 2sinx

cosx = 1/2

x = $$pi$$/3

$$\alpha$$ = $$pi$$/3 and 5$$pi$$/3

Not sure what I'm doing wrong.

The answer is $$pi$$/3 and 5$$pi$$/3 and 0, and $$pi$$

Thanks for the assistance, I greatly appreciate it.

 

[TbbZz]

Thanks for the help, rock.freak667 and HallsofIvy.

I got it now.