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Chapter 5: Problem 132

Write the trigonometric expression as an algebraic expression. $$\cos (2 \arccos x)$$

Short Answer

Expert verified
The algebraic expression for \( \cos (2 \arccos x) \) is \( 2x^2 - 1 \).

Step by step solution

01

Identify the formula to be used

Recall the formula for the cosine of double angle: \[ \cos(2A) = 2\cos^2(A) - 1 \] This can be used to solve the problem.
02

Substitute the value in the formula

Substitute \( A = \arccos x \) in the formula. Now, it becomes \[ \cos(2\arccos x) = 2\cos^2(\arccos x) - 1 \]
03

Simplify the expression

Remember that \( \cos(\arccos x) = x \). By substituting this into the formula, the expression simplifies to: \[ \cos(2\arccos x) = 2x^2 - 1 \]

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Most popular questions from this chapter

Solve the multiple-angle equation. $$\sin 2 x=-\frac{\sqrt{3}}{2}$$

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Write the expression as the sine, cosine, or tangent of an angle. $$\frac{\tan 45^{\circ}-\tan 30^{\circ}}{1+\tan 45^{\circ} \tan 30^{\circ}}$$

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