Question

СРОЧНО!!!!!!

 

sin(7п+x)=cos(9п+2 х)

Answer 1

sin(7п+x)=cos(9п+2 х)

sin(3*2pi+pi+x)=cos(4*2pi+pi+2x)

sin(pi+x)=cos(pi+2x)

-sinx==-cos2x

-sinx+cos2x=0

cos^2x-sin^2x-sinx=0

1-sin^2x-sin^2x-sinx=0

-2sin^2x-sinx+1=0 |*(-1)

2sin^2x+sinx-1=0

D=1+8=9

sinx1=-1+3/4=1/2

sinx2=-1-4/4=-1

 

при

sinx=1/2

x=arcsin1/2+Pin, n~Z

x=pi/6+pin, n~Z

 

при

sinx=-1

x=-pi/2+pin, n~Z

Ответ:  x=pi/6+pin, n~Z

x=-pi/2+pin, n~Z