In 2nd quadrant #90^0 < x >180^0 ,sinx=p/h=4/5 ; p=4 , h=5 :. b=- sqrt(5^2-4^2)= -3 :.cosx= b/h=-3/5#where #p# is perpedicular , #b# is base , #h# is hypotenuse.
In 3rd quadrant #180^0 < x >270^0 , cosy=b/h= -5/13 ; b= -5 , h=13 :. p=- sqrt(13^2-5^2)= -12 :.siny= p/h=-12/13#
#sin(x-y) =sinx*cosy-cosx*siny = 4/cancel5* (-cancel5/13) - (-3/5)* (-12/13) = -4/13 - 36/65 = -56/65#
#cos 2x= cos^2x- sin^2x= (-3/5)^2 - (4/5)^2 =9/25 -16/25 = -7/25#
#sin2y = 2*siny*cosy = 2* (-12/13) * (-5/13) =120/169 # [Ans]