Educator

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Example 1:

Use the double-angle formulas to find the sine and cosine of (2π /3). Use all three cosine formulas and check that the answers agree. Check that the answers agree with the sine and cosine of (2π /3) derived from the common values.

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Example 2:

Use the double-angle formulas to prove the following trigonometric identity:

sin2x = 2 tanx 1 + tan2 x

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Example 3:

Use the addition and subtraction formulas to derive a formula for tan2x in terms of tanx. Check the formula on x = (π /6).

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Example 4:

Use the double-angle formulas to find the sine and cosine of (4π /3). Use all three cosine formulas and check that the answers agree. Check that the answers agree with the sine and cosine of (2π /3) derived from the common values.

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Example 5:

Use the double-angle formulas to prove the following trigonometric identity:

sec2x = sec2 x 2 − sec2 x