Answer :

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 !!!


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