Problem 51 - Algebra and Trigonometry Real Mathematics, Real People

Question

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

Step-by-Step Solution

Answer

The algebraic expression for the given trigonometric expression is 1.

Step 1: Identify the Property

First, remember the special property that \(\arcsin x + \arccos x\) always equals \(\pi/2\). This property is derived from the fundamental relationship within a right-angle triangle where \(\sin^2 x + \cos^2 x = 1\).

Step 2: Apply the Property

Now replace \(\arcsin x + \arccos x\) in the expression with \(\pi/2\). Therefore, the given trigonometric expression simplifies to \(\sin(\pi/2)\).

Step 3: Compute the Expression

\(\sin(\pi/2)\) is 1, so the result of this expression is 1.