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

Question

exact answer i believe

Answer 1

sin(A-B) = sinAcosB-sinBcosA

A=tan^-1v

B=tan^-1u

substitute into the formula

sinA=sin(tan^-1v) = sin(sin^-1v/cos^-1v)

cosB= etc.

or just notice tan^-1v is the angle whose tangent is v. So let v = opposite side over adjacent side and sin(tan^-1v) = opposite side over hypotenuse = v/sqr1+v^2)

sin(A-B) then = v/sqr(1+v^2)(1/sqr(1+u^2) - 1/(sqr1+v^2)(u/sqr(1+u^2) = (v-u)/sqr(1+v2)sqr(1+u^2)