Дано: sin(п/3+t)+sin(п/3-t)=p найти sin(п/3+t) sin(п/3-t)

Question

Дано: sin(п/3+t)+sin(п/3-t)=p найти sin(п/3+t) sin(п/3-t)

Answer 1

2sinπ/3cost=p
2*√3/2cost=p
cost=p/√3
cos2t=2cos²t-1=2p²/3 -1
sin(π/3+t)sin(π/3-t)=1/2*(cos2t-cos2π/3)=1/2(cos2t+1/2=1/2*cos2t+1/4=
=1/2*2p²/3-1/2+1/4=p²/3-1/4