To Prove :

Formulae :

i)

ii)

iii)

iv)

v)

vi)

vii)

Answer :

Let,

Let

Therefore, y = s - t ………eq(1)

I. For

let

therefore,

Differentiating above equation w.r.t. x,

………

………….

………eq(2)

II. For

let

therefore,

Differentiating above equation w.r.t. x,

…………. By chain rule

………

………

………eq(3)

Differentiating eq(1) w.r.t. x,

………

………from eq(2) and eq(3)

= 2 tan^-1x

Hence proved !!!