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Double-Angle Formulas

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

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

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

sin 2x = 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 2x. Note that sin 2x = sin (x + x).

This formula comes from Problem 7.34.

8.3    Simplify the expression: .

Apply the double-angle ...

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