Question

sin2x + sin2y /sin2x - sin2y=tan(x+y)/tan(x-y)​

Answer 1

Step-by-step explanation:

sin(x-y)/cos(x-y)) / (sin(x+y)/cos(x+y))

(sinxcosy-cosxsiny)/(cosxcosy+sinxsiny)

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(sinxcosy+cosxsiny)/(cosxcosy-sinxsiny)

Expand those products, and you will be able to factor out some (sin^2+cos^2) and watch it become just like the left side.

Working on the left side first requires you to insert some canceling factors which are not obvious.