## Tag: proving

### Proving trigonometric identities #2

Problem: Prove that the equation below is an identity: 2 sin2Ө – sin4Ө = (1 – cos2Ө)(1 + cos2Ө). 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 sin2Ө…

### How to transform a pentagon into a triangle of the same area

This is the third in the series of problems involving transforming polygons into another polygon where the area is preserved. The first is about transforming a shape into another shape of the same area and the second is about transforming a quadrilateral into a triangle of the same area. The following problem builds on the…

### Angle inscribed in a semicircle

To solve the two problems below you need to know 1) The area of a circle is Πr2, with r as radius and that the area of a semicircle is of course  half of the circle, ½Πr2 and 2) the theorem the angle  in a semicircle theorem. Problem 1 Prove that the area of the solid…

### Proofs of sum of two even numbers is even

Problem Show that the sum of two even numbers is also an even number. Solutions 1. Good for 1/5 mark 2 + 4 = 6      6 + 8 = 14, 2+8 = 10      20 + 30 = 50 24 + 10 = 34. There’s no two even number I can think…