In trigonometry, the Cosine Rule (also known as Law of Cosine) relates the lengths of the sides of a triangle to the cosine of one of its angles. The following are three versions of the Cosine Formula. The easiest of course to remember is the last one since it looks like the Pythagorean Formula. The
Problem: Prove that the equation below is an identity: 2 sin2? – sin4? = (1 – cos2?)(1 + cos2?). Solution To prove that an equation is an identity, one must show that the Left Hand Side (LHS) of the equation is identical to its Right Hand Side (RHS). That is, LHS ? RHS. Proof LHS: 2 sin2?
To solve the two problems below you need to know 1) The area of a circle is ?r2, with r as radius and that the area of a semicircle is of course half of the circle, ½?r2 and 2) the angle in a semicircle theorem. Problem 1 Prove that the area of the solid green semicircle