sintan1 u tan1 v write the trigonometric expression as an al

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

Solution

sin(tan^-1u +tan^-1v)

sin(tan^-1(u+v)/(1-uv))

let tan^-1(u+v)/(1-uv) =a

tan a=u+v/(1-uv)

sin a= (u+v)/(sqrt((u+v)^2 +(1-uv)^2))

sin(tan^-1u +tan^-1 v)=(u+v)/(sqrt((u+v)^2 +(1-uv)^2))