The purpose of simplifying this expression is to reduce it to its simplest form, making it easier to work with and to solve for a specific value or variable.
To simplify this expression, we can use the trigonometric identity 2cos2x = cos2x + cos2x. This allows us to rewrite the expression as cos2x + cos2x - 2cosx. Then, we can factor out a common term of cosx to get cosx(cosx + 1) - 2cosx. Finally, we can further simplify by factoring out a cosx from the first two terms, giving us (cosx - 1)(cosx + 1).
When x=0, the expression becomes 2cos0 - 2cos0 = 2(1) - 2(1) = 0. Therefore, the value of the expression is 0 when x=0.
No, the expression (cosx - 1)(cosx + 1) is already in its simplest form and cannot be simplified any further.
Simplifying trigonometric expressions like this one can be useful in various real-world applications, such as engineering, physics, and astronomy. It allows for more efficient calculations and problem-solving by reducing complex expressions to simpler forms.