Math / Trigonometry

QuestionSimplify the expression (7.3)
7. $2 \sin 10 \theta \cos 10 \theta$

Studdy Solution

STEP 1

1. The expression involves trigonometric functions.
2. We are asked to simplify the expression using trigonometric identities.
3. The double angle identity for sine can be used here.

STEP 2

1. Identify the appropriate trigonometric identity.
2. Apply the identity to simplify the expression.

STEP 3

Recognize that the expression $2 \sin 10\theta \cos 10\theta$ can be simplified using the double angle identity for sine:
$\sin 2A = 2 \sin A \cos A$
In this case, $A = 10\theta$ .

STEP 4

Apply the double angle identity:
$2 \sin 10\theta \cos 10\theta = \sin(2 \times 10\theta)$
Which simplifies to:
$\sin(20\theta)$
The simplified expression is:
$\boxed{\sin(20\theta)}$

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