1)
sin50+sin70 =
= 2 sin (50+70)/2* cos(50-70)/2=
= 2 sin 60*cos10 = 2* √3/2 cos10= √3cos10
2)
sin27°+cos63°= sin(90°-63°)+cos63° = cos63°+ cos63°= 2 cos63°
3)
cos15° - cos75° = -2 sin(15°-75°)/2 sin(15°+75°)/2=
= -2 sin(-30°) sin45°= 2*0,5*√2/2 = √2/2
4)
cos(2П/3)-cos(3П/5) = -2 sin(2П/3-3П/5)/2 sin(2П/3+3П/5)/2=
= -2 sin(П/15)/2 sin(19П/15)/2=
= -2 sinП/30* sin19П/30
Возможно в условии одинаковые знаменатели, т.е. нужно cos(2П/5) вместо cos(2П/3).
Тогда решение такое:
cos(2П/5)-cos(3П/5)=
= -2 sin(2П/5-3П/5)/2 sin(2П/5+3П/5)/2=
= -2 sin(-П/10) sinП/2=
= 2*√2/2* sinП/10= √2/ sinП/10
5)
sin(π/12)-sin5π/12 =
= 2sin[(π/12-5π/12)/2]*cos[(π/12+5π/12)/2] =
=2sin(-π/6)*cosπ/4 =
= - 2sinπ/6*cosπ/4 = -2*1/2*√2/2*= -√2/2
13 + (17 + а) = 13 + 17 + а = 30 + а
(х + 25) + 42 = х + 25 + 42 = х + 67
(36 + у) + 54 = 36 + у + 54 = у + 90
(а + 38) - 19 = а + 38 - 19 = а + 19
(59 + х) - 29 = 59 + х - 29 = х + 30
23 - (17 + у) = 23 - 17 - у = 6 - у
(а + 115) - 21 = а + 115 - 21 = а + 94
63 - (х + 12) = 63 - х - 12 = 51 - х
54 - (27 + у) = 54 - 27 - у = 27 - у
(а + 59) - 59 = а + 59 - 59 = а
73 - (х + 55) = 73 - х - 55 = 18 - х
31 - (12 + у) = 31 - 12 - у = 19 - у
(54 + х) - 16 = 54 + х - 16 = 38 + х
65 - 35 - у = 30 - у
45 + b - 13 = 32 + b
55 - (с + 23) = 55 - с - 23 = 32 - с
m - 35 - 42 = m - 77
38 - n + 12 = 50 - n
(р - 52) + 73 = р - 52 + 73 = р + 21
а - 26 - 14 = а - 40