Question

Write the trigonometric expression as an algebraic expression containing u and v.

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

Answer 1

Using sin(A-B)= sinAcosB - cos AsinB

Sin(tan^-1 u- tan-1 v)=
sin(tan^-1u)cos(tan^-1v)-cos(tan^-1u)s…

Now if an angle has a tanx= u/1,
then the hypotenuse is sqr(u^2+1),
so sin x = u/sqr(u^2+1) and cosx= 1/sqr(u^2+1)


sin(tan^-1u)cos(tan^-1v)-cos(tan^-1u)s…
[u/sqr(u^2+1)][1/sqr(v^2+1)]- [1/sqr(u^2+1)][v/sqr(v^2+1)]......

= (u-v)/[sqr(u2+1)][sqr(v^2+1)]

Now you can simplify.

Answer 2

Stuff like this makes me dizzy.

Answer 3

@natalia0207 Do you follow?