2)сosx=-5/13
sinx=√(1-cos²x)=√(1-25/169)=√(144/169)=12/13
3)cos78cos18+sin78sin18=cos(78-18)=cos60=1/2
sin58cos13-cos58sin13=sin(58-13)=sin45=√2/2
4)sin(x/2)=-1⇒x/2=-π/2+2πn⇒x=-π+4πn
2cos²x-cosx-1=0
cosx=a
2a²-a-1=0
D=1+8=9
a1=(1-3)/4=-1/2⇒cosx=-1/2⇒x=+-2π/3+2πn
a2=(1+3)/4=1⇒cosx=1⇒x=2πn
5)cos²x+sinx=3
1-sin²x+8sinx-3=0
sin²x-8sinx+2=0
sinx=a
a²-8a+2=0
D=64-8=56
a1=(8-2√14)/2=4-√14⇒sinx=4-√14⇒x=(-1)^n*arcsin(4-√14)+πn
a2=4+√14⇒sinx=4+√14>1 нет решения