\\it\ is\ given\ that\\\\ cos\ k\theta =2\cos\theta \cos(k-1)\theta-\cos(k-2)\theta\\\\ show\ that\\ \\ \cos2\theta=2\cos^2\ \theta-1\\ \cos3\theta=4\cos^3\ \theta-3\ \cos\theta\\ \cos4\theta=8\cos^4\theta -8\cos^2\theta+1\\\\ The\ T\ polynomials\ are\ defined\ by\ the\ recurrence\ formula \\\\...