(coefficients (* (+ (cos α) (* i (sin α))) (+ (cos β) (* i (sin β)))) i) ;{(+ (* (cos α) (cos β)) (* -1 (sin α) (sin β))) (+ (* (cos α) (sin β)) (* (sin α) (cos β)))} ;(cos (+ α β)) = (+ (* (cos α) (cos β)) (* -1 (sin α) (sin β))) ;(sin (+ α β)) = (+ (* (cos α) (sin β)) (* (sin α) (cos β))) (coefficients (* (+ (cos α) (* i (sin α))) (- (cos β) (* i (sin β)))) i) ;{(+ (* (cos α) (cos β)) (* (sin α) (sin β))) (+ (* -1 (cos α) (sin β)) (* (sin α) (cos β)))} ;(cos (- α β)) = (+ (* (cos α) (cos β)) (* (sin α) (sin β))) ;(sin (- α β)) = (+ (* -1 (cos α) (sin β)) (* (sin α) (cos β))) (coefficients (+ (* (+ (cos α) (* i (sin α))) (+ (cos β) (* i (sin β)))) (* (+ (cos α) (* i (sin α))) (- (cos β) (* i (sin β))))) i) ;{(* 2 (cos α) (cos β)) (* 2 (sin α) (cos β))} ;(* (cos α) (cos β)) = (* (/ 1 2) (+ (cos (+ α β)) (cos (- α β)))) ;(* (sin α) (cos β)) = (* (/ 1 2) (+ (sin (+ α β)) (sin (- α β)))) (coefficients (- (* (+ (cos α) (* i (sin α))) (+ (cos β) (* i (sin β)))) (* (+ (cos α) (* i (sin α))) (- (cos β) (* i (sin β))))) i) ;{(* -2 (sin α) (sin β)) (* 2 (cos α) (sin β))} ;(* (sin α) (sin β)) = (* (/ -1 2) (- (cos (+ α β)) (cos (- α β)))) ;(* (cos α) (sin β)) = (* (/ 1 2) (- (sin (+ α β)) (sin (- α β)))) (coefficients (** (+ (cos α) (* i (sin α))) 3) i) ;{(+ (cos α)^3 (* -3 (cos α) (sin α)^2)) (+ (* 3 (cos α)^2 (sin α)) (* -1 (sin α)^3))} ;(cos (* 3 α)) = (+ (cos α)^3 (* -3 (cos α) (sin α)^2)) ; = (+ (* 4 (cos α)^3) (* -3 (cos α))) ;(sin (* 3 α)) = (+ (* 3 (cos α)^2 (sin α)) (* -1 (sin α)^3)) ; = (+ (* -4 (sin α)^3 (* 3 (sin α))))