Question

prove that (tan (x+y)-tan x)/(1+tan (x+y)tanx)​

Answer 1

Answer:

To Prove:

tan(x−y)=

1+tanxtany

tanx−tany

We know that:

tanA=

cosA

sinA

tan(x−y)=

cos(x−y)

sin(x−y)

tan(x−y)=

cosxcosy+sinxsiny

sinxcosy−cosxsiny

Dividing Numeator and denominator by (cosxcosy):

tan(x−y)=

cosxcosy

cosxcosy+sinxsiny

cosxcosy

sinxcosy−cosxsiny

tan(x−y)=

1+tanxtany

tanx−tany

Hence Proved.