14) x²+y²-2x+2y-7=0⇒x²-2x+1+y²+2y+1-9=0⇒(x-1)²+(y+1)²=3²
O=(1;-1); r=3
16) x²+y²+4x-8y+19=0⇒x²+4x+4+y²-8y+16-1=0⇒(x+2)²+(y-4)²=1
O=(-2;4); r=1
a) 1 +sin2x =1+2sinx*cosx = sin²x +cos²x +2sinx*cosx =(cosx+sinx)².
б) 1 -sin2x =1-2sinx*cosx = sin²x +cos²x -2sinx*cosx =(cosx-sinx)².
в) (sinπ/12)*(cosπ/12) =(1/2)*2*(sinπ/12)*(cosπ/12) =(1/2)*(sin2*(π/12) ) =
(1/2)*(sinπ/6)=(1/2)*((1/2) =1/4.
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тождества:
sin²α +cos²α =1.
sin2α =2sinα*cosα ⇒sinα*cosα =(sin2α) /2 .