1. 2sin^2x - (2a+1)*sinx + a = 0 2. (a-1)*cosx + (a+1)*sinx = 2a 3. sin^4x + cos^4x + sin2x = a , ! с полным решением

(1-cos2x)²/4+(1+cos2x)²/4=sinxcosx

1-2cos2x+cos²2x+1-2cos2x+cos²2x-4sinxcosx=0

2+2cos²2x-2sin2x=0

2sin²2x+2cos²2x+2cos²2x-2sin2x=0

2sin²2x+4cos²2x-2sin2x=0

2sin²2x+4-4sin²2x-2sin2x=0

2sin²2x+2sin2x-4=0

sin²2x+sin2x-2=0

sin2x=a

a1+a2=-1 u
a1*a2=-2

a1=-2⇒sin2x=-2∉[-1; 1]

a2=1⇒sin2x=1⇒2x=π/2+2πn

x=π/4+πn

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