Draw a right triangle.
Designate an acute angle, Angle a.
Label the legs consistent with the given value of the tangent of 'a'.
Contemplate the hypotenuse.
You have essentially said at the beginning of the question (correctly):
In order for both sides of the equation to be equal, both sides have to have
This means that, looking at the right hand side, .
Both sides have to have .
So, looking at the right hand side,
And then it's just an application of