![sin(3x)*cos(x)=sin(2,5x)*cos(1,5x);\\ 0.5*(sin(3x-x)+sin(3x+x))=0.5*(sin(2.5x-1.5x)+sin(2.5x+1.5x));\\ sin(3x-x)+sin(3x+x)=sin(2.5x-1.5x)+sin(2.5x+1.5x);\\ sin (2x)+sin(4x)=sin x+sin (4x);\\ sin(2x)=sin x;\\ sin (2x)-sin x=0;\\ 2sin x cos x-sin x=0;\\ sin x(2cos x-1)=0;](https://tex.z-dn.net/?f=sin%283x%29%2Acos%28x%29%3Dsin%282%2C5x%29%2Acos%281%2C5x%29%3B%5C%5C+0.5%2A%28sin%283x-x%29%2Bsin%283x%2Bx%29%29%3D0.5%2A%28sin%282.5x-1.5x%29%2Bsin%282.5x%2B1.5x%29%29%3B%5C%5C+sin%283x-x%29%2Bsin%283x%2Bx%29%3Dsin%282.5x-1.5x%29%2Bsin%282.5x%2B1.5x%29%3B%5C%5C+sin+%282x%29%2Bsin%284x%29%3Dsin+x%2Bsin+%284x%29%3B%5C%5C+sin%282x%29%3Dsin+x%3B%5C%5C+sin+%282x%29-sin+x%3D0%3B%5C%5C+2sin+x+cos+x-sin+x%3D0%3B%5C%5C+sin+x%282cos+x-1%29%3D0%3B)
остюда либо
k є Z
либо
n є Z
ответ: <var>
k є Z,
n є Z</var>
64a³+(2-a)³=(4a+(2-a))(16a²-4a(2-a)+(2-a)²)=(3a+2)(16a²-8a+4a²+4+a²-4a²)=(3a+2)(17a²-8a+4)
1/cos^2+3 tgx -5=0
(sin^ + cos^)/cos^2+3 tgx -5=0
tg^x +1 +3 tgx -5=0
tgx=t
t^2 +3t -4=0
D=25
t1=-4 ; tgx=-4 ; x1=2пи*n -19/45*пи , n E Z
t2=1 ; tgx=1 ; x2= пи*n + пи/4 , n E Z
ОТВЕТ
x1=2пи*n -19/45*пи , n E Z
x2= пи*n + пи/4 , n E Z