sina*sinb/cosa*cosb=1
sina*sinb=cosa*cosb
-sina*sinb+cosa*cosb=0
cos(a+b)=0
a+b=kπ+π/2
sinb=sin(kπ+π/2-a)
=±sin(π/2-a)
=±cosa
所以sina*sinb=±sina*cosa
=±sin2a/2
所以sina*sinb最大值=1/2