Solving a system of two trigonometric equations

[FlatAssembler]

So, in our Control Engineering classes, in the presentation about synthesizing a regulator using Bode plot (using lead compensation and lag compensation), we have the following system of equations:

omega_lb1 / omega_ln1 = 12.6
atan(2 / omega_lb1) - atan(2 / omega_ln1) = -6 deg

Allegedly, the solution is:

omega_lb1 = 0.2 rad/sec
omega_ln1 = 0.016 rad/sec

But how can that system of equations be solved?

[The Valkyrie]

With beer!

Lots of beer.

[FlatAssembler]

I have also asked this question on StackExchange: https://math.stackexchange.com/q/4702617/791819

[The Valkyrie]

Did they recommend beer, too?

[Angrboda]

I'm sure drugs of some kind were involved.

[FlatAssembler]

Did they recommend beer, too?

Sean Roberson there told me:

Solve for one variable in the first equation (there's a clear choice), and then use the formula for the tangent of a difference.

I don't understand that. Maybe you do?

[Angrboda]

Did they recommend beer, too?

Sean Roberson there told me:

Solve for one variable in the first equation (there's a clear choice), and then use the formula for the tangent of a difference.

I don't understand that. Maybe you do?

We could tell you, but then we'd have to kill you.

[Ravenshire]

FA, why won't you just do your own damned homework instead of asking others to do it for you? Cheating your way through school only hurts yourself.

[The Valkyrie]

Sean Roberson there told me:

I don't understand that. Maybe you do?

We could tell you, but then we'd have to kill you.

Slowly.

[FlatAssembler]

FA, why won't you just do your own damned homework instead of asking others to do it for you? Cheating your way through school only hurts yourself.

What do you think is the point of school? The point of school is not to learn useful skills. The point of school is to give you a diploma, a piece of paper which is supposed to help you get hired.