Express cos 3 theta in terms of cos theta Solutioncos3theta

Express cos 3 theta in terms of cos theta

Solution

cos(3theta) = cos(2theta + theta) = cos2theta cos theta - sin2theta sin theta

                                                             = (2 cos²theta -1)cos theta - 2sin theta cos theta* sin theta

                                                             = 2cos³theta -costheta -2sin²theta cos theta

                                                              = 2cos theta (cos²theta-sin²theta) -cos theta

                                                             = 2 cos theta* cos 2theta -cos theta

                                                             = cos theta(2cos 2 theta -1)

                                                              = cos theta(4cos²theta-3)

                                                               =4cos³theta -3cos theta