a is the opposite side b is the adjacent side c is the hypotenuse. x is the angle Problem: expression for sin x as a function of a and c. Solution: Identities taken from textbooks: sin x = a/b (1) tan x = a/c (2) sin x = sqrt(tan^2 x / (1 + tan^2 x)) (3) substituting (2) in (3), we have sin x = a / sqrt(a^2 + c^2) (4) On the other hand, a^2 + b^2 = c^2 => b=sqrt(c^2 - a^2) substituting this in (1), we have sin x = a / sqrt(-a^2 + c^2) (5) (4) != (5) ????? how come? What's wrong here, please?