Explain how the tangents of complementary angles are related.

  tan(α) = 1/tan(90°-α)

Step-by-step explanation:

The tangent of one is the reciprocal of the tangent of the other.

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In a right triangle, ...

  tan = opposite/adjacent

For the two complementary acute angles in such a triangle, opposite and adjacent are swapped. That is the tangent of one is the inverse of the tangent of the other. (That inverse is also known as the cotangent.)

  tan(α) = cot(90°-α) = 1/tan(90°-α)

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