Question

tan(x+y)=3/4 & tan(x - y)=1/3, find tan 2x

Answer 1

hello users ....

################################

we have given that:-
tan (x+y) = 3/4 and  tan (x-y) = 1/3

we have to find:
tan 2x = ?

solution :-
we know that :

$tan^{-1} x + tan^{-1}y = tan^{-1} [ \frac{x +y}{1 - xy } ]$

Here;
tan (x+y) = 3/4  

=>$(x + y) = tan^{-1} \frac{3}{4}$    .........(1.)

and

tan (x -y) = 1/3

=> $(x - y) = tan^{-1} [ \frac{1}{3}]$    ............(2.)

now ;
adding (1.) and(2.), we get ;

= 2x = $tan^{-1} \frac{3}{4} + tan^{-1} \frac{1}{3}$

=> $tan^{-1} [ \frac{ \frac{3}{4} + \frac{1}{3} }{1 - \frac{3}{4} * \frac{1}{3} } ]$

=> $tan^{-1}[ \frac{ \frac{13}{12} }{ \frac{9}{12} } ]$

=> $tan^{-1}[ \frac{13}{9} ]$

=> 2x = $tan^{-1}[ \frac{13}{9} ]$

=> tan 2x = 13 / 9 answer 

##############################################

✪✪ hope it helps ✪✪

Answer 2

Step-by-step explanation:

tan(x+y)=3/4 & tan(x-y)=1/3, find 2x=?