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
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sinx^2=1-cosx^2=1-0.36=0.64 sinx=-0.8 sinx=0.8
sinx^2=1-0=1 sinx=-1 sinx=1
tgx=3/4 cosx^2=1/(1+tgx^2)=1/(1+9/16)=1/(25/16) cosx^2=16/25 cosx=-4/5 cosx=4/5 2cosx=-8/5 2cosx=8/5
tgx=pi cos^2x=1/1+0=1 cosx^2=1 cosx=+-1 2cosx=+-2
7xy-14xy^3=7xy (1-2y^2)
-a^3b-ab=ab (-a^2-1)
-24n-18n^3=6n (-4-3^2)
15a^2-12a^4=3a^2 (5-4a^2)
-6b+12b^2+6b^5=6b (-1+2b+b^4)
2a (x-y)-b (x-y)=(x-y)(2a-b)
4x (a+b)-3 (a+b)^2=(a+b)(4x-3)