cos(pi*1/7+a)*cos(5*pi*1/14-a)-sin(pi*1/7+a)*sin(5*pi*1/14) если a=1/4 (упростите выражение)

$$- sin{left (frac{5 pi}{14} right )} sin{left (a + frac{pi}{7} right )} + cos{left (- a + frac{5 pi}{14} right )} cos{left (a + frac{pi}{7} right )}$$

$$- sin{left (frac{5 pi}{14} right )} sin{left (a + frac{pi}{7} right )} + cos{left (- a + frac{5 pi}{14} right )} cos{left (a + frac{pi}{7} right )}$$

cos(pi/7 + (1/4))*cos((5*pi)/14 – (1/4)) – sin(pi/7 + (1/4))*sin((5*pi)/14)

$$- sin{left (frac{5 pi}{14} right )} sin{left ((1/4) + frac{pi}{7} right )} + cos{left (- (1/4) + frac{5 pi}{14} right )} cos{left ((1/4) + frac{pi}{7} right )}$$

cos(pi/7 + 1/4)*cos((5*pi)/14 – 1/4) – sin(pi/7 + 1/4)*sin((5*pi)/14)

$$- sin{left (frac{5 pi}{14} right )} sin{left (frac{1}{4} + frac{pi}{7} right )} + cos{left (frac{1}{4} + frac{pi}{7} right )} cos{left (- frac{1}{4} + frac{5 pi}{14} right )}$$

cos(1/4 + pi/7)*sin(1/4 + pi/7) – sin(5*pi/14)*sin(1/4 + pi/7)

$$- sin{left (frac{5 pi}{14} right )} sin{left (frac{1}{4} + frac{pi}{7} right )} + sin{left (frac{1}{4} + frac{pi}{7} right )} cos{left (frac{1}{4} + frac{pi}{7} right )}$$

$$sin{left (a + frac{pi}{7} right )} cos{left (a + frac{pi}{7} right )} – sin{left (frac{5 pi}{14} right )} sin{left (a + frac{pi}{7} right )}$$

-0.900968867902419*sin(pi/7 + a) + cos(pi/7 + a)*cos((5*pi)/14 – a)

$$sin{left (a + frac{pi}{7} right )} cos{left (a + frac{pi}{7} right )} – sin{left (frac{5 pi}{14} right )} sin{left (a + frac{pi}{7} right )}$$

$$- sin{left (frac{5 pi}{14} right )} sin{left (frac{1}{7} left(7 a + piright) right )} + cos{left (frac{1}{14} left(- 14 a + 5 piright) right )} cos{left (frac{1}{7} left(7 a + piright) right )}$$

/ /pi / pi / pi
|- cos|–| + cos|a + –||*sin|a + –|
7 / 7 // 7 /

$$left(cos{left (a + frac{pi}{7} right )} – cos{left (frac{pi}{7} right )}right) sin{left (a + frac{pi}{7} right )}$$

$$- frac{1}{2} sin{left (a right )} – frac{1}{2} sin{left (a + frac{2 pi}{7} right )} + frac{1}{2} sin{left (2 a + frac{2 pi}{7} right )}$$

/ /5*pi / pi / pi
|- sin|—-| + cos|a + –||*sin|a + –|
14 / 7 // 7 /

$$left(cos{left (a + frac{pi}{7} right )} – sin{left (frac{5 pi}{14} right )}right) sin{left (a + frac{pi}{7} right )}$$

/ pi / pi /5*pi / pi
cos|a + –|*sin|a + –| – sin|—-|*sin|a + –|
7 / 7 / 14 / 7 /

$$sin{left (a + frac{pi}{7} right )} cos{left (a + frac{pi}{7} right )} – sin{left (frac{5 pi}{14} right )} sin{left (a + frac{pi}{7} right )}$$

/ / pi / 2*pi
sin|2*|a + –|| sin|a + —-|
7 // sin(a) 7 /
————— – —— – ————-
2 2 2

$$- frac{1}{2} sin{left (a right )} + frac{1}{2} sin{left (2 left(a + frac{pi}{7}right) right )} – frac{1}{2} sin{left (a + frac{2 pi}{7} right )}$$

/ /pi /pi / /5*pi /5*pi / /pi /pi /5*pi
|cos(a)*cos|–| – sin(a)*sin|–||*|cos(a)*cos|—-| + sin(a)*sin|—-|| – |cos(a)*sin|–| + cos|–|*sin(a)|*sin|—-|
7 / 7 // 14 / 14 // 7 / 7 / / 14 /

$$left(- sin{left (frac{pi}{7} right )} sin{left (a right )} + cos{left (frac{pi}{7} right )} cos{left (a right )}right) left(sin{left (frac{5 pi}{14} right )} sin{left (a right )} + cos{left (frac{5 pi}{14} right )} cos{left (a right )}right) – left(sin{left (a right )} cos{left (frac{pi}{7} right )} + sin{left (frac{pi}{7} right )} cos{left (a right )}right) sin{left (frac{5 pi}{14} right )}$$