(a) Write the standard expression for cos2θ in terms of sinθ and cosθ.
(b) Eliminate sin2θ from your answer in (a) by using an appropriate trigonometric identity and hence obtain a form of cos2θ involving only cosθ.
(c) Eliminate cos2θ from your answer in (a) in a similar manner and hence obtain a form of cos2θ involving only sinθ.
(d) Give a brief explanation (about two sentences) to justify why the three expressions obtained in parts (a), (b) and (c) are identically equal for every real value of θ.