求证sin3*sin1=sin^2(2)-sin^2(1)
问题描述：
求证sin3*sin1=sin^2(2)-sin^2(1)
答
左边=sin(2+1)sin(2-1)
=(sin2cos1+cos2sin1)(sin2cos1-cos2sin1)
=sin²2cos²1-cos²2sin²1
=sin²2(1-sin²1)-(1-sin²2)sin²1
=sin²2-sin²2sin²1-sin²1+sin²2sin²1
=sin²2-sin²1
=右边
命题得证