Thinking- (10 points) SUPPOSE that 2 cos2 x + 4 sin x cos x = a sin 2x + b cos 2x + c is an identity, determine the values of a, b, c. [HINT: USE the fact that it is an identity to substitute suitable values of x on both sides of the equation. Some of the unknowns a, b, c may get eliminated depending on what is substituted. Or, the substitutions will lead to a linear system that can be solved.](2 points) Is it always possible to prove every trigonometric identity? EXPLAIN your