**Double-Angle Formulas**

Ditch the 2s in sin 2x and cos 2y

**8.1** Express sin 2*x* as a product of single-angle trigonometric functions.

The expression sin 2*x* is described as a “double angle,” because the argument of the expression is 2*x* rather than simply *x*. The identity below allows you to rewrite the double-angle expression sin 2*x* as the product of two single-angle expressions.

sin 2*x* = 2 sin *x* cos *x*

**8.2** Verify your answer to Problem 8.1 by applying the sum formula for sine.

Apply the sum formula for sine to expand sin 2*x*. Note that sin 2*x* = sin (*x* + *x*).

This formula comes from Problem 7.34.

**8.3** Simplify the expression: .

Apply the double-angle ...

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