Final answer:
To solve the trigonometric equation involving cos(x) and sin(x), we obtain a common denominator and use trigonometric identities to simplify the expression. The provided values for x appear to be unrelated to this equation and are not used in this solution.
Step-by-step explanation:
To solve the given equation -cos(x)/(1-sin(x)) + cos(x)/(1+sin(x)), we use the properties of trigonometric expressions and combine the fractions. As we look to simplify the expression, our goal is to have a common denominator. Given two fractions, / and /, with common numerators but different denominators, we combine them by obtaining the product of the denominators (⋅) to serve as the new common denominator.
To combine -cos(x)/(1-sin(x)) and cos(x)/(1+sin(x)), we multiply the numerator and denominator of the first fraction by (1+sin(x)) and the second fraction by (1-sin(x)). This results in equivalent expressions with a common denominator, which can then be added or subtracted as necessary. We use trigonometric identities, such as sin^2(x) + cos^2(x) = 1, to further simplify expressions.
The provided example values x = 0.0216 or x = -0.0224 seem to be solutions to a different problem and don't relate to the initial equation asked to be solved. Thus, they are not considered in the solution to the given equation. Finally, the task is to simplify the original expression, which does not inherently yield a specific numeric solution for x without additional parameters.