Prove that the trignometric ratios does not depend on sides of the triangle
False statement!
The 6 trig ratios are explicitly defined by the ratio formed by pairs of the sides of a right-angled triangle.
If you refer to right-angled triangles, then if the sides of one right-angled triangles are x, y, and r and the sides of another right-angled triangle are
xk, yk, and rk, then the two triangles are similar, since the corresponding
sides are in the same ratio.
e.g. in first triangle: cos Ø = x/r
in the 2nd triangle: cos Ø = xk/(rk) = x/r
so this for the other 5 trig ratios