Question

prove that tan-1 ( x+rootx/ 1- x3/2 ) =Tan-1x

Answer 1

We know that tan(x+y)=[tan x + tan y]/[1-tan x*tan y]

Let tan x =a and tan y=b

Thus

x=tan-1 a

y=tan-1 b

Thus…tan-1 a+tan-1 b=tan-1[(a+b)/1-ab)]…eqn(1)

As [√x]^3=x√x

Thus…in the question…

a=x

b=√x

Plug in these two values in eqn(1) to get the required result

Hope it helps