Question

if tan(x+y) =3 by 4and tan (x-y)=1 by 3 ,then find tan 2x

Answer 1

tan(x+y)=3/4
tan(x-y)=1/3
so (x+y)=tan^-1(3/4)---------(1)
(x-y)=tan^-1(1/3)------------(2)
add (1) and (2) equation
then you will get 2x=tan^1(3/4) +tan^-1(1/3)
accrding to formula tan^-1(X)+tan^-1(Y)=tan^-1{(X+Y)/(1-(X*Y))}
then 2x=tan^-1(13/9)
may be this will help u guys.

Answer 2

Answer:

Step-by-step explanation:

solu: As ,

2x =(x+y)+(x-y)

given,

tan(x+y) =3 by 4 ; tan(x-y) = 1 by

tanA = tan (x+y)+ tan (x-y) by

1-tan (x+y) . tan (x-y).}formula

tanA = (3/4) + (1/3) by 1-/ (3/4) (1/3)

tanA = 13/9

formula : tan2x = 2tanA by 1- tan²A

. = 2*(13/9) by 1-(3/9)²

tan2x = -117/44