Рассмотрим сразу числитель: sin 10 cos 55 + sin 280 sin 55 = sin 10 cos 55 + sin (270 + 10) sin 55 = [формулы приведения] = sin 10 cos 55 + (-cos 10) sin 55 = [sin (a-b) = sin a cos b - sin b cos a] = sin (10 - 55) = sin (-45) = - sin 45 = -√2/2 Знаменатель: sin 10 cos 110 + sin 260 cos 200 = sin 10 cos (90 + 20) + sin (270 - 10) cos (180 +20) = sin 10 (-sin 20) + (-cos 10) (-cos 20) = cos 10 cos 20 - sin 20 sin 10 = [cos(a+b) = cos a cos b - sin a sin b] = cos (10+20) = cos 30 = √3/2 Все выражение: √6 * (-√2/2) / (√3/2) = -√6*√2*2 / (2√3) = -√2 * √2 = -2
4 / 2 2 /atan2(-im(m), -re(m))\ 4 / 2 2 /atan2(-im(m), -re(m))\
\/ 3 *\/ im (m) + re (m) *cos|| i*\/ 3 *\/ im (m) + re (m) *sin||
\ 2 / \ 2 /
n1 = - -
3 3
4 / 2 2 /atan2(-im(m), -re(m))\ 4 / 2 2 /atan2(-im(m), -re(m))\
\/ 3 *\/ im (m) + re (m) *cos|| i*\/ 3 *\/ im (m) + re (m) *sin||
\ 2 / \ 2 /
n2 = +
3 3
/ / \\ / / \\
/ 2 2 | |im(m) \/ 3 *re(m) re(m) \/ 3 *im(m)|| / 2 2 | |im(m) \/ 3 *re(m) re(m) \/ 3 *im(m)||
/ / \ / \ |atan2| - + || / / \ / \ |atan2| - + ||
/ |im(m) \/ 3 *re(m)| |re(m) \/ 3 *im(m)| | \ 6 6 6 6 /| / |im(m) \/ 3 *re(m)| |re(m) \/ 3 *im(m)| | \ 6 6 6 6 /|
n3 = - 4 / | - | + | + | *cos|| - i*4 / | - | + | + | *sin||
\/ \ 6 6 / \ 6 6 / \ 2 / \/ \ 6 6 / \ 6 6 / \ 2 /
/ / \\ / / \\
/ 2 2 | |im(m) \/ 3 *re(m) re(m) \/ 3 *im(m)|| / 2 2 | |im(m) \/ 3 *re(m) re(m) \/ 3 *im(m)||
/ / \ / \ |atan2| - + || / / \ / \ |atan2| - + ||
/ |im(m) \/ 3 *re(m)| |re(m) \/ 3 *im(m)| | \ 6 6 6 6 /| / |im(m) \/ 3 *re(m)| |re(m) \/ 3 *im(m)| | \ 6 6 6 6 /|
n4 = 4 / | - | + | + | *cos|| + i*4 / | - | + | + | *sin||
\/ \ 6 6 / \ 6 6 / \ 2 / \/ \ 6 6 / \ 6 6 / \ 2 /
/ / \\ / / \\
/ 2 2 | |im(m) \/ 3 *re(m) re(m) \/ 3 *im(m)|| / 2 2 | |im(m) \/ 3 *re(m) re(m) \/ 3 *im(m)||
/ / \ / \ |atan2| + - || / / \ / \ |atan2| + - ||
/ |im(m) \/ 3 *re(m)| |re(m) \/ 3 *im(m)| | \ 6 6 6 6 /| / |im(m) \/ 3 *re(m)| |re(m) \/ 3 *im(m)| | \ 6 6 6 6 /|
n5 = - 4 / | + | + | - | *cos|| - i*4 / | + | + | - | *sin||
\/ \ 6 6 / \ 6 6 / \ 2 / \/ \ 6 6 / \ 6 6 / \ 2 /
/ / \\ / / \\
/ 2 2 | |im(m) \/ 3 *re(m) re(m) \/ 3 *im(m)|| / 2 2 | |im(m) \/ 3 *re(m) re(m) \/ 3 *im(m)||
/ / \ / \ |atan2| + - || / / \ / \ |atan2| + - ||
/ |im(m) \/ 3 *re(m)| |re(m) \/ 3 *im(m)| | \ 6 6 6 6 /| / |im(m) \/ 3 *re(m)| |re(m) \/ 3 *im(m)| | \ 6 6 6 6 /|
n6 = 4 / | + | + | - | *cos|| + i*4 / | + | + | - | *sin||
\/ \ 6 6 / \ 6 6 / \ 2 / \/ \ 6 6 / \ 6 6 / \ 2 /
sin 10 cos 55 + sin 280 sin 55 = sin 10 cos 55 + sin (270 + 10) sin 55 = [формулы приведения] = sin 10 cos 55 + (-cos 10) sin 55 = [sin (a-b) = sin a cos b - sin b cos a] = sin (10 - 55) = sin (-45) = - sin 45 = -√2/2
Знаменатель:
sin 10 cos 110 + sin 260 cos 200 = sin 10 cos (90 + 20) + sin (270 - 10) cos (180 +20) = sin 10 (-sin 20) + (-cos 10) (-cos 20) = cos 10 cos 20 - sin 20 sin 10 = [cos(a+b) = cos a cos b - sin a sin b] = cos (10+20) = cos 30 = √3/2
Все выражение:
√6 * (-√2/2) / (√3/2) = -√6*√2*2 / (2√3) = -√2 * √2 = -2