The number of solutions of the equation21cos cos cos 2 ,3 3 4x x x  

To find the number of solutions of the equation 21cos(cos(2x)) = 3/4, we can follow these steps:

Step 1: Simplify the equation: 21cos(cos(2x)) = 3/4

Step 2: Take the inverse cosine of both sides to eliminate the outer cosine function: cos(cos(2x)) = (3/4) / 21

Step 3: Solve for the inner cosine function: cos(2x) = arccos((3/4) / 21)

Step 4: Use the double angle identity for cosine: 2x = ±arccos((3/4) / 21)

Step 5: Divide both sides by 2 to solve for x: x = ±(1/2) * arccos((3/4) / 21)

Step 6: Calculate the value of arccos((3/4) / 21) and simplify the expression further if needed.

Step 7: Substitute the calculated value of arccos((3/4) / 21) into the equation x = ±(1/2) * arccos((3/4) / 21) to find the solutions for x.

Step 8: Determine the number of solutions based on the values obtained in step 7.