The number of solution(s) of the equation 24sinx−10cosx=x2−4x+2018 is/are

This problem involves a trigonometric equation and a quadratic equation. Here are the steps to solve it:

Step 1: Rewrite the equation The given equation is 24sinx - 10cosx = x^2 - 4x + 2018.

Step 2: Analyze the equation The left side of the equation involves trigonometric functions (sin and cos), while the right side is a quadratic equation. This makes it difficult to solve directly.

Step 3: Simplify the equation Unfortunately, there is no straightforward way to simplify this equation due to the combination of trigonometric and quadratic terms.

Step 4: Graphical solution One possible approach to find the number of solutions is to graph both sides of the equation and see where they intersect.

Step 5: Use a graphing tool You can use a graphing tool to plot y = 24sinx - 10cosx and y = x^2 - 4x + 2018.

Step 6: Find the intersection points The number of times these two graphs intersect will give the number of solutions to the equation.

Please note that this is a complex problem and may not have a simple solution. It's also possible that it may not have any real solutions, depending on the graphs.