а) Обратимся к формуле синуса суммы углов: sin$\alpha +\beta$ = sin$\alpha$cos$\beta$ + cos$\alpha$sin$\beta$.

а) sin$\pi /15$cos$4\pi /15$ + cos$\pi /15$sin$4\pi /15$ = sin$\pi /15+4\pi /15$ = sin$\pi /3$ = √3/2.

б) cos$123°$cos$78°$ + sin$123°$sin$78°$ = cos$123°-78°$ = cos$45°$ = 1/√2.

а) −cos$\alpha +\beta$ − sin$\beta$sin$\alpha$ = - $cos(\alpha )cos(\beta )-sin(\alpha )sin(\beta )$ - sin$\beta$sin$\alpha$ = -cos$\alpha$cos$\beta$ + sin$\alpha$sin$\beta$ - sin$\beta$sin$\alpha$ = -cos$\alpha$cos$\beta$ + sin$\beta$sin$\alpha$ - sin$\beta$sin$\alpha$ = -cos$\alpha$cos$\beta$ - sin$\beta$sin$\alpha$.

б) cos$x-2\pi /3$ - √3/2 sin$x$ = cos$x$cos$2\pi /3$ + sin$x$sin$2\pi /3$ - √3/2 sin$x$ = cos$x$ $-1/2$ + sin$x$ √3/2 - √3/2 sin$x$ = -1/2 cos$x$ + √3/2 sin$x$ - √3/2 sin$x$ = -1/2 cos$x$.