数学题求证：[sinq(1+sinq)+cosq(1+cosq)
求证：[sinq(1+sinq)+cq(1+cosq)]×[sinq(1-sinq)+cosq(1-cosq)] = sin2q
证：左边 = (sinq+sin2q+cosq+cos2q)×(sinq-sin2q+cosq-cos2q) = (sinq+ cosq+1)×(sinq+cosq -1) = (sinq+ cosq)2 -1 = 2sinqcosq = sin2q = 右边 ∴原式得证