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1)sin(3x-2x)=sin2x
sinx-sin2x=0
sinx-2sinxcosx=0
sinx(1-2cosx)=0
sinx=0⇒x=πn
cosx=1/2⇒x=+ - π/3+2πn
2)2sin5xcos2x-2cos2x=0
2cos2x(sin5x-1)=0
cos2x=0⇒2x=π/2+πn⇒x=π/4+πn/2
sin5x=1⇒5x=π/2+2πn⇒x=π/10+πn/5
3)2cos^4x+1-3(2cos²x-1)=0
2cos^4x+1-6cos²x+3=0
2cos^4x-6cos²x+4=0
cos^4x-3cos²x+2=0
a=cos²x, a²-3a+2=0, a1+a2=3 U a1*a2=2
a1=1,cos²x=1⇒cosx=1, x=2πn U cosx=-1, x=π+2πn
a2=2,cos²x=2⇒cosx=√2∉[-1;1]-нет решения и cosx=-√2∉[-1;1]- нет решения
3х+5y-6x-5y=21-27
-3x=-6
x=2
3*2+5y=21
5y=21-6
5y=15
<span>1) y=3
2) 3x+5*3=21
3x=6
x=2
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1/2cos2x+1/2cos4x-cos2x=0
1/2cos4x-1/2cos2x=0
1/2*(2cos²2x-1)-1/2cos2x=0
cos²2x-1/2cos2x-1/2=0
cos2x=a
a²-0,5a-0,5a=0
D=0,25+2=2,25
a1=(0,5-1,5)/2=-0,5⇒cos2x=-0,5⇒2x=+-5π/6+2πn⇒x=+-5π/12+πn
a2=(0,5+1,5)/2=1⇒cos2x=1⇒2x=2πn⇒x=πn