Some problems provide the opportunity for more than one mistake.

The Goal

Solve the equation:

The Mistakes

Find the mistakes:

1.

(Roll the mouse over the math to see a hint in red)

2.

(Roll the mouse over the math to see a hint in red)

3.

(Roll the mouse over the math to see a hint in red)

The Correction

(Roll the mouse over the area above to see the correction in blue)

Explanations

In the first mistake an incorrect formula was used for cos(2x). Eventually the equation reduces to a form that we cannot solve algebraically.

The second attempted solution has three mistakes, the first and third of which involve the use of incorrect formulas for cos(2x). The second mistake is the replacement of the fraction 3/2 by 6 (for some reason the product of 3 and 2 was computed).

In the third mistake once again an incorrect formula was used for cos(2x).

The keys to solving this problem are knowing the correct double angle formulas and then using correct algebra to solve the equation.