А) sin П/5+sin 3П/5
Б) cos 2П/3+сos п/6
В) sin 3П/10-sin П/10
Г) cos П/4-сos 3П/4
Б) cos 2П/3+сos п/6
В) sin 3П/10-sin П/10
Г) cos П/4-сos 3П/4
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Answers & Comments
А) sin П/5+sin 3П/5=2sin(П/5+3п/5)/2 *соs(П/5-3п/5)/2=2sin2п/5соsп/5
Б) cos 2П/3+сos п/6=2соs(2п/3+п/6)/2*соs(2п/3-п/6)/2= =2соs5п/12*соsп/4 = 2((√6-√2)/4)*(√2/2) = (√2(√6-√2))/4= (√12-2)/4
В) sin 3П/10-sin П/10=2sin(3П/10-п/10)/2 *соs(3П/10+п/10)/2=2sinП/10 *соsп/5
Г) cos П/4-сos 3П/4=-2sin(п/4+3п/4)/2sin(П/4-3п/4)/2 =2sinп/2*sinп/4=2*1*(√2/2)=√2