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Write the following expression as the sine, cosine, or tangent of a double-angle. Then find the exact value...

Write the following expression as the sine, cosine, or tangent of a double-angle. Then find the exact value of the expression.
2 tan π / (1 - tan^2 π)

Answer

The expression 2 tan π / (1 - tan^2 π) is the formula for tan(2θ), where θ = π.

Since tan(π) = 0, we have:

  1. 2 tan π = 2 * 0 = 0
  2. tan^2 π = 0^2 = 0
  3. 1 - tan^2 π = 1 - 0 = 1

Therefore, the expression simplifies to:

0 / 1 = 0

The exact value of the expression is 0.

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