Question

prove 

sin( x y ) / sin ( x - y )=tan x tan y / tan x -tany

Answer 1

$\huge{Hey Mate!!!}$

sin(x+y) / sin(x-y)  (expand both of them)

sinxcosy + cosxsiny /sinxcosy - cosxsiny

( divide the whole by COSXCOSY) so we get as following

=(sinxcosy+cosxsiny) /cosxcosy

  (sinnxcosy-cosxsiny) / cosxcosy  (we get)

=tanx+tany / tanx-tany

Hope it helps.

Answer 2

$\huge{Hey mate }$

The answer of u r question is..✌️✌️

✨Sin (xy)/sin (x-y) = tan x tan y /tan x - tan y.

Ans:✍️✍️✍️✍️✍️✍️✍️✍️✍️

$\large {Given,}$

$\frac{sin \: x + y}{sin \: x - y}$

$= \frac{sin \: x \: cos \: y}{sin \: x \: cos \: y - \: cos \: x \: sin \: y}$

divide the whole by cos x cos y

$= \frac{sin \: x \: cos \: y \: cos \: x \: sin \: y}{ \frac{cos \: x \: cos \: y \: sin \: x \: cos \: y \: - \: os \: x \: sin \: y \: }{cos \: x \: cos \: y} }$

$= \frac{tan \: x \: + \: tan \: y}{tan \: x - \: tan \: y}$

Thank you..⭐️⭐️