Put x = tanθ

⇒ θ = tan^–1(x)

tan^–1{–tanθ }

= tan^–1{–tanθ }

= tan^–1{secθ –tanθ }

= tan^–1

= tan^–1

Sinθ = ,cosθ =

= tan^–1

= tan^–1

= tan^–1

Dividing by we get

= tan^–1

= tan^–1

= tan^–1

tan(x–y) =

= tan^–1

=

From 1 we get

= ^.

Therefore, the simplification of given equation is ^.