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Anti-trigonometric Function

Source: 1985 National High School Mathematics League, Exam One, Problem 3

February 23, 2020
function

Problem Statement

If arccos⁡45−arccos⁡(−45)=arcsin⁡x\arccos\frac{4}{5}-\arccos\left(-\frac{4}{5}\right)=\arcsin x, then (A)x=2425(B)x=−2425(C)x=0(D)\text{(A)}x=\frac{24}{25}\qquad\text{(B)}x=-\frac{24}{25}\qquad\text{(C)}x=0\qquad\text{(D)} No such xx
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