Перепишем так:
sin 4b + sin 10b + sin 22b + sin 16b = (sin 4b + sin 22b) + (sin 10b + sin 16b)
Есть формула:
![sin (x)+sin(y)=2sin \frac{x+y}{2}*cos \frac{x-y}{2}](https://tex.z-dn.net/?f=sin+%28x%29%2Bsin%28y%29%3D2sin+%5Cfrac%7Bx%2By%7D%7B2%7D%2Acos+%5Cfrac%7Bx-y%7D%7B2%7D++)
2sin(13b)*cos(9b) + 2sin(13b)*cos(3b) = 2sin(13b)*(cos 9b + cos 3b)
Можно еще применить формулу:
![cos(x)+cos(y)=2cos \frac{x+y}{2}*cos \frac{x-y}{2}](https://tex.z-dn.net/?f=cos%28x%29%2Bcos%28y%29%3D2cos+%5Cfrac%7Bx%2By%7D%7B2%7D%2Acos+%5Cfrac%7Bx-y%7D%7B2%7D++)
2sin(13b)*2cos(6b)*2cos(3b) = 4sin(13b)*cos(6b)*cos(3b)
Решение во вложении................
= ( V 18 ) * ( V 2 ) + ( V 3 ) * ( V 2 ) - 0,5 ( V 24 ) = ( V 36 ) + ( V 6 ) - ( 0,5 * 2 ) V 6 = 6 + ( V 6 ) - ( V 6 ) .= 6