Answer the following questions concerning the double–angle identity for cosine.
(a) Write the three standard equivalent forms of cos2θ.
(b) Which of the forms in part (a) is most suitable for replacing sin2θ in an expression? Give a brief reason for your choice.
(c) Using the form selected in part (b), transform sin4θ into a sum involving only cosine functions of multiple angles, with no power of sine or cosine higher than one.