соsa+cos2a+cos6a+cos7a=

cosα+cos2α+cos6α+cos7α=(cosα+cos7α)+(cos2α+cos6α)==2·cos(α+7α)/2·cos((α-7α)/2+2·cos(2α+6α)/2·cos(2α-6α)/2==2cos4α·cos(-3α)+2·cos4α·cos(-2α)==2·cos4α·(cos3α+cos2α)=2cos4α·2·cos5α/2·cosα/2==4cos4α·cos5α/2·cosα/2;