T0(x)=cos(0cos−1x)=1T_0(x)=cos(0cos^{-1}x)=1T0(x)=cos(0cos−1x)=1
T1(x)=cos(cos−1x)=xT_1(x)=cos(cos^{-1}x)=xT1(x)=cos(cos−1x)=x
T2(x)=cos(2cos−1x)=2cos2(cos−1x)−1=2x2−1T_2(x)=cos(2cos^{-1}x)=2cos^2(cos^{-1}x)-1=2x^2-1T2(x)=cos(2cos−1x)=2cos2(cos−1x)−1=2x2−1
T3(x)=cos(3cos−1x)=4cos3(cos−1x)−3cos(cos−1x)=4x3−3xT_3(x)=cos(3cos^{-1}x)=4cos^3 (cos^{-1}x)-3 cos (cos^{-1}x)= 4x^3-3xT3(x)=cos(3cos−1x)=4cos3(cos−1x)−3cos(cos−1x)=4x3−3x
T4(x)=cos(4cos−1x)=2cos2(2cos−1x)−1=2(2cos2(cos−1x)−1)2−1=8cos4(cos−1x)−8cos2(cos−1x)+2−1=8x4−8x2+1T_4(x)=cos(4cos^{-1}x)=2cos^2(2 cos^{-1}x) -1=2(2cos^2(cos^{-1}x)-1)^2-1=8cos^4 (cos^{-1}x)-8cos^2 (cos^{-1}x)+2-1= 8x^4-8x^2+1T4(x)=cos(4cos−1x)=2cos2(2cos−1x)−1=2(2cos2(cos−1x)−1)2−1=8cos4(cos−1x)−8cos2(cos−1x)+2−1=8x4−8x2+1
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