Question

cos2a+cos14a+cos6a+cos10a

Answer 1

$(cos2a+cos14a)+(cos6a+cos10a)= \ \ =2*cos frac{2a+14a}{2}*cos frac{2a-14a}{2}+2*cos frac{6a+10a}{2}*cos frac{6a-10a}{2}= \ \ = 2cos8a*cos6a + 2cos8a*cos2a=2cos8a(cos6a+cos2a)=\ \ =2cos8a*2cos4a*cos2a=4cos8a*cos4a*cos2a.$