write the trigonometric expression as an algebraic expression containing u and v. sin(tan^-1(u)+tan^-1(v)

Answer 1

tan¹ of a number is an angle, need to use sin(A+B) formula

given tan^-1u is angle , the angle is part of right triangle and has opposite side u and adjacent side 1.

sin(tan^-1u)=u/√(1+u²) and cos(tan^-1u)=1/√(1+u²)

same idea with v

correction

sin(tan^-1(u)+tan^-1(v))=[u/√(1+u²) ]*[(1/√(1+v²)]+[v/√(1+v²)]*[(1/√(1+u²)]

=[u+v]*[(1+u²)*(1+v²)]^-(1/2)