Verified answer

if cos Ɵ = m/n

then, the adjacent side is: m

the hypotenuse is: n

so, the opposite side is: ? (use the Pythagorean theorem...

did you get √(n^2 - m^2) ?

tan Ɵ = [√(n^2 - m^2)]/m

qed

If cos Ɵ = m/n, then sin Ɵ = √(n^2 - m^2)/n.

So tan Ɵ = √(n^2 - m^2)/m