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;