Question

b) Prove that tan^-1- x + tan^-1-y = x+y/1-xy ​

Answer 1

Answer:

Step-by-step explanation:

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Tan⁻¹x  + Tan⁻¹y   = Tan⁻¹( (x + y) /( 1  - xy))

Step-by-step explanation:

To be Proved

Tan⁻¹x  + Tan⁻¹y  = Tan⁻¹((x + y)/(1 - xy) )

Let say

Tan⁻¹x  + Tan⁻¹y  =  M

Taking Tan both sides

TanM = Tan (Tan⁻¹x  + Tan⁻¹y )

Tan(A + B) = (TanA + TanB)/(1 - TanATanB)

A = Tan⁻¹x   & B =Tan⁻¹y

=> TanM = (Tan(Tan⁻¹x) + Tan(  Tan⁻¹y) )/( 1  - Tan(Tan⁻¹x)Tan(Tan⁻¹y))

=> TanM = (x + y) /( 1  - xy)

=> M = Tan⁻¹( (x + y) /( 1  - xy))

M = Tan⁻¹x  + Tan⁻¹y  

=> Tan⁻¹x  + Tan⁻¹y   = Tan⁻¹( (x + y) /( 1  - xy))

QED

Proved