When proving an identity, you may manipulate only one side of the equation throughout. You may not use normal algebraic techniques to manipulte both sides. Let's begin with the identity you wish to prove. cos2x - sin2x ?=? 2cos2x - 1 We know that sin2x + cos2x = 1 (Pythagorean Identity). Therefore, sin2x = 1 - cos2x. Substituting for sin2x, we may write cos2x - (1 - cos2x) ?=? 2cos2x - 1 cos2x - 1 + cos2x ?=? 2cos2x - 12cos2x -1 = 2cos2x - 1 The identity is proved. (Note that once the identity is proved, you may remove the question marks from around the equal sign.)
Cannot prove that 2 divided by 10 equals 2 because it is not true.
You can't it equals 2. You can't it equals 2.
No you can not prove that 9 +10 = 21.
No, but there is a way to prove that zero equals one.
Using faulty logic.
It is not possible to prove it because it is not true!
You cannot prove it since it is axiomatic. You can get consistent theories (matrix algebra, for example) where ab is not ba.
Using a calculator
4,4,4,4 = 20