解;由题意可知,x=sinα,y=cos2α=1-2sin²α,∴y=1-2x²,∴y`=-4x,设切线为y-2=kx,切点为（X0,Y0）【0是脚标】,∴k=-4X0,∴Y0-2=-4X0²∴Y0=2-4X0²,且Y0=1-2X0²,∴2Y0=2-4X0²=Y0,∴Y0=0,...