1)=4* (cos(π/12-x+π/12+x) +cos(π/12 -x-π/12-x)) /2=2*(cos2π/12 +cos(-x))=
=2(cosπ/6 + cosx)=2*(1/2+cosx)=1+2cosx;
2)=4*(cos(π/3-x-π6-x) -cos(π/3-x+π/6+x)) /2=2(cos(π/6-2x) - cos3π/6)=
=2(cos(π/6-2x) -cosπ/2)=2cos(π/6-2x); cosπ/2=0
4) =4sin16a cos(π/2-4a)=4(cos(16a-π/2+4a) -cos(16a+π/2-4a) /2=2(cos(20a-π/2) -cos(12a+π/2)=2(sin20a - sin12a)
смотри формулы "преобразование произведений триг. функций в суммы!