Answer:
Step-by-step explanation:
Let a = tan⁻¹(x), so tan(a) = x,
[tex]\sin(a)=\frac{x}{\sqrt{1+x^2}}, \cos(a)=\frac{1}{\sqrt{1+x^2}},[/tex]
Let b = tan⁻¹(y), so tan(b) = y,
[tex]\sin(b)=\frac{y}{\sqrt{1+y^2}}, \cos(b)=\frac{1}{\sqrt{1+y^2}},[/tex]
sin( tan⁻¹(x) + tan⁻¹(y)) = sin(a + b)
= sin(a) cos(b) + cos(a)sin(b)
= [tex]\frac{x}{\sqrt{1+x^2}}\times\frac{1}{\sqrt{1+y^2}}+ \frac{y}{\sqrt{1+y^2}}\times\frac{1}{\sqrt{1+x^2}}[/tex]
[tex]=\frac{x+y}{\sqrt{(1+x^2)(1+y^2)}}[/tex]
