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TrigonometrySuperchallengeInverse Trigonometric Functions

Inverse Trigonometric Functions · Superchallenge problem

How many ordered pairs of integers (a,b)(a,b) satisfy arccos⁡a14+arccos⁡b14=2π3\arccos\dfrac{a}{14}+\arccos\dfrac{b}{14}=\dfrac{2\pi}{3}?