Solve each equation for x.
arccos x + arctan 1 = 11π/12

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Recognize that the equation is given as \(\arccos x + \arctan 1 = \frac{11\pi}{12}\), and our goal is to solve for \(x\).

Recall the value of \(\arctan 1\). Since \(\tan \frac{\pi}{4} = 1\), it follows that \(\arctan 1 = \frac{\pi}{4}\).

Substitute \(\arctan 1 = \frac{\pi}{4}\) into the equation to get \(\arccos x + \frac{\pi}{4} = \frac{11\pi}{12}\).

Isolate \(\arccos x\) by subtracting \(\frac{\pi}{4}\) from both sides: \(\arccos x = \frac{11\pi}{12} - \frac{\pi}{4}\).

Simplify the right side by finding a common denominator and then use the definition of arccosine to write \(x = \cos\left(\arccos x\right) = \cos\left(\frac{11\pi}{12} - \frac{\pi}{4}\right)\).

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