Cos ( 1/3 phi + a) cos a + sin (1/3 phi + a ) sin a =....

TriGonoMetRi

cos a cos b + sin a sin b
= cos (a - b)

••
cos (1/3 π + a) cos a + sin (1/3 π + a) sin a
= cos (1/3 π - a) ✔
= cos (60° - a)
= cos 60 cos a + sin 60° sin a
= 1/2 (cos a + √3 sin a) ✔