Question

Prove that tan inverse x +tan inverse y=tan inverse x+y by 1-xy

Answer 1

Hi friend this is your answer

Answer 2

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

Learn more:

a and tan (theta alpha)

https://brainly.in/question/9738618

If 2 sin x = sin y and 2 cos x = 3 cos y then find the value of tan (x + y)

https://brainly.in/question/10685245

prove that tan(x+y)=tanx+tany/1-tanxtany - Brainly.in

https://brainly.in/question/4804542