Educator

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Example 1:

Use the half-angle formulas to find the sine and cosine of 15^° . Check that the answers satisfy the Pythagorean identity sin² x + cos² x = 1.

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Example 2:

Prove the following trigonometric identity:

cos 1 2 x + sin 1 2 x cos 1 2 x − sin 1 2 x = secx + tanx

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Example 3:

Prove the following half-angle formula for tangents. Be careful about removing any ± signs!

tan 1 2 x = 1− cosx sinx

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Example 4:

Use the half-angle formulas to find the sine and cosine of (π /8). Check that the answers satisfy the Pythagorean identity sin² x + cos² x = 1.

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Example 5:

Prove the following trigonometric identity:

tanx tan 1 2 x = secx − 1