The quantity cos2θ can be written in several equivalent ways. Study the following and respond:
a. (i) Write any three standard algebraic forms of cos2θ in terms of sinθ and cosθ.
b. (ii) Explain, with reasons, which of the three forms is most convenient when only sinθ is known and which is most convenient when only cosθ is known.
c. (iii) Give one brief numerical illustration (no detailed computation required) to support the explanation in part (ii).