Prove sin^2(x)-cos^2(y)/Sinx cosx-Sinycosy=TAN(x+y)

Answer 1

recall that
sinxcosx - sinycosy = cos(x+y)

LS = (sin^2(x)-cos^2(y))/(Sinx cosx-Sinycosy)
notice I inserted the absolutely necessary brackets to make the statement true
= (sinx + cosy)(sinx - cosy)/(cos(x+y))
not getting anywhere
≠ tan(x+y)

I usually test the equation with some arbitrary values, should have done it before I tried proving it

I used x = 78° and y=23°
and the equation was not satisfied.
All you need is ONE exception and the equation is NOT an identity.