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let cos(x+y) = 4/5 and sin(x-y) = 5/13 then tan2x =
tan 2x = tan(x+y + x-y)
={tan(x+y)+tan(x-y)}/(1-tan(x+y)tan(x-y))
={3/4+5/12}/(1-3/4*5/12)
=56/33
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