Write each of the following in the simplest form:

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 ^{.}

7