prove that :- sin 2x - sin 2y/cos 2y - cos 2x = cot (x+y)
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sin2x-sin2y/cos2y-cos2x
={2cos(2x+2y)/2sin(2x-2y)/2}/{2sin(2y+2x)/2sin(2x-2y)/2}
[∵, sinC-sinD=2cos(C+D)/2sin(C-D)/2 and cosC-cosD=2sin(C+D)/2sin(D-C)/2]
=cos(x+y)sin(x-y)/sin(x+y)sin(x-y)
=cot(x+y) (Proved)
={2cos(2x+2y)/2sin(2x-2y)/2}/{2sin(2y+2x)/2sin(2x-2y)/2}
[∵, sinC-sinD=2cos(C+D)/2sin(C-D)/2 and cosC-cosD=2sin(C+D)/2sin(D-C)/2]
=cos(x+y)sin(x-y)/sin(x+y)sin(x-y)
=cot(x+y) (Proved)
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