50(cos39cos21+cos129cos69) =50{cos39cos21+cos(90+39)cos(90-21)} =50(cos39cos21-sin39sin21) =50cos(39+21) =50cos60 =25

How does $\cos39\cos 21+\cos 120\cos 69\implies$ the next step?

@ above when I first saw this question we note that it looks very similar to $cos(a+b)$ or $cos(a-b)$ after that we take the necessary to steps to transform it. I also noted that $39+21=60$ which is friendly, thus it was intuitive to continue from that poitn