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Chapter 5: Problem 53

Write the trigonometric expression as an algebraic expression. $$\sin (\arcsin x+\arccos x)$$

Short Answer

Expert verified
The algebraic expression for the given trigonometric expression is \(1\).

Step by step solution

01

Recognize inverse trigonometric relationship

Observe the identities of \(\arcsin x\) and \(\arccos x\) which are inverse functions of each other. This implies that \(\arcsin x + \arccos x = \frac{\pi}{2}\).
02

Substitute and simplify

Substitute \(\frac{\pi}{2}\) into the original equation. The original equation \(\sin (\arcsin x+\arccos x)\) hence becomes \(\sin \frac{\pi}{2}\).
03

Final simplification

Since \(\sin \frac{\pi}{2} = 1\), the final solution is \(1\)

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