3)a) sinx=√2/2; x=(-1)^k*arcsin(√2/2)+pik; k-целое
x=(-1)^k*pi/4+pik
б)cos2x=1/2; 2x=+-arccos(1/2)+2pin;n-целое
2x=+-pi/3+2pin; x=+-pi/6+pin
в)tg2x=0; 2x=arctg0+pik; 2x=0+pik=pik; x=pik/2
г)4sin^2x-3sinx-1=0; пусть sinx=t; 4t^2-3t-1=0;D=9+16=25
t1=(3+5)/8=1; sinx=1; x=(-1)^k*pi/2+pik
t2=(3-5)/8=-1/4; sinx=-1/4; x=(-1)^n*arcsin(-1/4)+pin
д)5x/3+pi/6=+-arccos(1/2)+2pin; n-целое
5x/3+pi/6=+-pi/3+2pin
5x/3=+-pi/3-pi/6+2pin;
a)5x/3=pi/3-pi/6+2pin=pi/6+2pin;x=(3/5)(pi/6+2pin)=pi/10+6pin/5 б)5x/3=-pi/3-pi/6+2pin=-pi/2+2pin;x=(3/5)(-pi/3+2pin)= -pii/5+6pin/5
4)cos2a=1-2sin^2a=1-2*(4/5)^2=1-2*16/25=1-32/25=-7/25