1) sin 82° 30' cos 37° 30'
sina+sinb=2sin(a+b/2)*cos(a-b/2)
a+b/2=82,5
a-b/2=37,5
a+b=165
a-b=75
a=165-b
165-b-b=75
-2b=-90
b=45
a=120
(1/2)* 2sin 82° 30' cos 37° 30'=(sin120+sin45)/2=(sin(180-60)+sin45)/2=(sin60+sin45)/2=(sqrt(3)/2+sqrt(2)/2)/2=((sqrt(3)+sqrt(2))/2)/2=(sqrt(3)+sqrt(2))/4
2) 2sin 3a cos 4a + sin a = sin 7a
sina1+sinb=2sin(a1+b/2)*cos(a1-b/2)
a1+b/2=3a
a1-b/2=4a
a1+b=6a
a1-b=8a
a1=6a-b
6a-b-b=8a
-2b=2a
b=-a
a1=6a+a=7a
2sin 3a cos 4a + sin a = sin 7a
sin7a+sin(-a)+sina=sin7a
sin7a-sina+sina=sin7a
sin7a=sin7a
3) 4cos a/2 cos a sin 3a/2 = sin a + sin 2a + sin 3a
2*2cosa cosa/2 sin3a/2=sina + sin2a + sin3a
2*(cosa/2 + cos 3a/2)*sin3a/2=sina + sin2a + sin3a
2 cosa/2 * sin3a/2 + 2 cos3a/2 sin3a/2 = sina + sin2a + sin3a
2 cosa/2 * sin3a/2 + sin3a = sina + sin2a + sin3a
sin a + sin 2a + sin 3a = sina + sin2a + sin3a
Объяснение:
y'=2x-7