Trigonometric equations involving multiple trigonometric functions can appear daunting at first, but with the right strategies, they can be effectively solved. One powerful method is to use trigonometric identities and properties to simplify the equation before attempting to find the solution.

For instance, consider the equation 2sin(x) + tan(x) = 3cos(x). We can start by rewriting the equation using sine and cosine identities: 2sin(x) + sin(x)/cos(x) = 3cos(x). Then, we can multiply through by cos(x) to eliminate the fraction, resulting in 2sin(x)cos(x) + sin(x) = 3cos^2(x).

Next, we can use the double angle identities to rewrite sin(2x) and cos(2x) in terms of sin(x) and cos(x). By substituting these identities, the equation becomes sin(2x) + sin(x) = 3(1 - sin^2(x)).

At this point, we have transformed the initial equation into one that involves only a single trigonometric function. We can now apply algebraic techniques to solve for sin(x) and subsequently find the values of x.

Remember, practice is key when it comes to tackling advanced trigonometric equations. Keep working through examples and don't hesitate to seek assistance if you need it. You've got this!