Find the exact solution of the equation.
\[
20 \cos ^{-1} x-4 \pi=4 \cos ^{-1} x
\]

The solution set is $\{\square$.
(Simplify your answer, including any radicals. Type an exact answer, using radicals as needed.)

Answer

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Answer

$\boxed{\{\frac{\sqrt{2}}{2}\}}$ is the final answer.

Steps

Step 1 ：Given the equation $20 \cos ^{-1} x-4 \pi=4 \cos ^{-1} x$.

Step 2 ：Move the term with 'x' on one side and the constant term on the other side.

Step 3 ：Solve the equation to isolate 'x'.

Step 4 ：The solution to the equation is $x = \frac{\sqrt{2}}{2}$.

Step 5 ：$\boxed{\{\frac{\sqrt{2}}{2}\}}$ is the final answer.