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= sen(x-y) sen(x+y)
= ( senx cosy - cosx seny ) ( senx cosy + cosx seny )
= (senx cosy)² + (senx cosy cosx seny) - (cosx seny senx cosy) - (cosx seny)²
= sen²(x) cos²(y) + 0 - cos²(x) sen²(y)
= sen²(x) [ 1 - sen²(y) ] - sen²(y) [ 1 - sen²(x) ]
= sen²(x) - sen²(x) sen²(y) - sen²(y) + sen²(y) sen²(x)
= sen²(x) - sen²(y)
con eso ya quedaría demostrado. Éxitos.