1) sinα / 2cosα/2 = 2sinα/2 *cosα/2 / 2cosα/2 = sinα/2 .
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2) cosα /(sinα/2 -cosα/2) = (cos²α/2 - sin²α/2) /(sinα/2 -cosα/2)=
(cosα/2 + sinα/2)*(cosα/2 - sinα/2)) /(sinα/2 -cosα/2) = -(cosα/2 + sinα/2).
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3) 1 - 2sin²(45°+1,5α) =cos2(45°+1,5α) =cos(90°+3α) = - sin3α .
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4) sinα/2*cosα/2*cosα =(1/2)sinα*cosα =(1/4)sin2α. * * * sin2α / 4 * * *
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5) sin3α /sinα +cos3α/cosα =(sin3α*cosα+cos3*αsinα) / sinα*cosα =
sin(3α+α) / (1/2)*sin2α =2sin4α /sin2α =2*2sin2α*cos2α / sin2α = 4cos2α.
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6) (ctqα -tqα) / (ctqα -tqα) =(cosα/sinα -sinα/cosα) /(cosα/sinα +sinα/cosα) =
(cos²α - sin²α) / (cos²α + sin²α ) =cos2α.
7) (sin²2α - 4sin²α) /(sin²2α +4sin²α -4) =
(4sin²α *cos²α - 4sin²α) /(4sin²α*cos²α - 4(1-sin²α) ) =
4sin²α (cos²α - 1) / (4sin²α*cos²α - 4cos²α) =
4sin²α (cos²α - 1) / 4cos²α (sin²α*-1) =-4sin⁴α /(-4cos⁴α ) =tq⁴α.
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8) (2cos²α -1) /(2ctq(π/4 -α)*cos²(π/4 +α) =
cos2α / 2tq(π/4 +α) *cos²(π/4 +α)=cos2α / 2sin(π/4 +α) *cos(π/4 +α) =
cos2α / sin2(π/4 +α) = cos2α / sin(π/2 +2α) = cos2α / cos2α =1.