№2
a)sin(a+b)+sin(a+b)=2sin((a+b+a-b)/2)*cos((a+b-a+b)/2)=2*sina*cosb
б)sin(605)*cosb+sinb*cos835=sin65*cosb+sinb*cos(pi-65)=
=sin65*cosb+sinb*cos65=sin(65+b)
605=360+180+65; 835=360+360+115; 115=180-65
в)0.25sin(405+b)*cos(b+765)=0.125(sin(405+b+b+765)+sin(405+b-b-765))=0.125(sin(2b+1170)+sin(-360))=0.125*sin(2b)
г)sin4a*cos3a+sin3a*cos4a-sin(6pi-a)=sin7a-sina=2cos4a*sin3a
д)(sin(1.5pi+a)+sin(2pi+a))/(2cos(-a)*sin(-a)+1)=(sina-cosa)/(1-sin2a)
e)sin2a/(1+cos2a)=2*sina*cosa/(1+2(cosa)^2-1)=sina/cosa=tga
ж)4sin15*cos15*sin100=2sin30*sin100=cos70-cos130
№3
a)sin(pi+x)=cos(-pi/3)
-sinx=1/2
x=arcsin(-0.5)+2pi*n и x=pi-arcsin(-0.5)+2pi*n
x=-pi/6+2pi*n и x=7pi/6+2pi*n
б)cos4x*sin3a+sin4a*cos3a=1
sin7x=1
7x=pi/2+pi*n
x=pi/14+pi*n/7
№4
а)sina/(1-cosa)=(1+cosa)/sina
(sina)^2=1-(cosa)^2
(sina)^2+(cosa)^2=1
1=1
в)1/(tga+ctga)=sina*cosa
tga+ctga=1/(sina*cosa) =>
sina*cosa=sina*cosa
1=1