1)сosx·cosy=(1/2)·(cos(x-y)+cos(x+y))
sinx·siny=(1/2)·(cos(x-y)+cos(x+y))
cos54·cos6-sin54·sin6=(1/2)·(cos48+cos60)-(1/2)·(cos48-cos60)=(1/2)·cos60+(1/2)·cos60=cos60=1/2
cos(3π/10)·cos(π/20)+sin(π/20)·sin(3π/10)=(1/2)·(cos(5π/20)+cos(7π/20)+(1/2)·(cos(-5π/20)-cos(7π/20))=(1/2)·cos(5π/20)+(1/2)·(cos(5π/20))=cos(π/4)=√2/2
2)sin(3x+2y)·cos(x+2y)-sin(x+2y)·cos(3x+2y)=(1/2)·(sin(3x+2y+x+2y)+sin(3x+2y-x-2y))-(1/2)·(sin(x+2y+3x+2y)+sin(x+2y-3x-2y))=(1/2)·(sin(4x+4y)+sin(2x))-(1/2)·(sin(4x+4y)+sin(-2x))=(1/2)·sin2x-(1/2)·sin(-2x)=sin2x