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Chapter 5: Problem 29

Use a double-angle formula to rewrite the expression. $$6 \sin x \cos x$$

Short Answer

Expert verified
The expression, when rewritten using the double-angle formula, is \(3 \sin 2x\).

Step by step solution

01

Apply the Double-Angle Formula

First, identify where the double angle formula can be applied in the equation. Here, the double angle formula for sine (\(2 \sin x \cos x = \sin 2x\)) fits, but the given expression is \(6 \sin x \cos x\), not \(2 \sin x \cos x\). Thus, the coefficient '6' should be divided by '2' in order to properly apply the double-angle formula.
02

Divide by Coefficient

Divide the given equation, \(6 \sin x \cos x\), by 2 which results in \(3 \sin 2x\).
03

Substitute with Double-Angle Formula

Now substitute the double-angle formula for sine into the equation. The left hand side, after dividing by 2, simplifies to \(3 \sin 2x \).

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