I recently read that two students have proven the Pythagorean Theorem using Trigonometry.
I haven't looked at their proof, but the problem seems straight forward.
Consider a right triangle with sides a and b and hypotenuse c, and angle theta opposite side a.
Then the tan(theta) = a/b.
sine(theta) = a/c.
So c = a/sine(theta) = a/sine(arctan(a/b).
Using Mathematica:

a/Sin[ArcTan[a/b]] evaluates to Sqrt[1 + a^2/b^2] b

which is equivalent to Sqrt[a^2 +b^2]

    In[1]:= a/Sin[ArcTan[a/b]]

    Out[1]= Sqrt[1 + a^2/b^2] b

Am I missing something ?