Hello all, I was wondering if someone has ever found a purely algebraic proof for the addition/subtraction theorems of trigonometry, mainly sin(a+b)=sin(a)cos(b)+sin(b)cos(a). Given a right triangle: Let x be one of the perpendicular legs and let the other leg be composed of two parts, y1 and y2. Let the line that separates angle a from angle b also be the line that separates y1 from y2 when it intersects with the perpendicular leg. Let a line segment that is perpendicular to the hypotenuse be drawn to intersect with the leg composed of y1 and y2. Call the parts of the hypotenuse on each side of the line z1 and z2 respectively. Eq1) (z1+z2)^2 = x^2 + (y1+y2)^2 Eq2) x^2 + y1^2 = z1^2 + y2^2 - z2^2 Prove: (y1+y2)/(z1+z2)=(y1z1)/(x^2 + y1^2) + (x(y2^2 - z2^2)^0/5)/(x^2 + y1^2) 1) Any thoughts? 2) Is using latex preferable?