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Simplify (tan 35°44′14″)/(1 − tan² 35°44′14″).

Simplify the tan of 35 degrees 44 minutes and 14 seconds divided by one minus tan squared of 35 degrees 44 minutes and 14 seconds.

In order to answer this question, we need to recall one of our double-angle formulae. The tan of two 𝜃 is equal to two multiplied by the tan of 𝜃 divided by one minus tan squared 𝜃. By dividing both sides of this equation by two, we have the tan of two 𝜃 divided by two is equal to the tan of 𝜃 divided by one minus tan squared 𝜃.

The right-hand side of our equation looks similar to the expression in the question, where 𝜃 is equal to 35 degrees 44 minutes and 14 seconds. Multiplying both sides of this equation by two, we see that two 𝜃 is equal to 71 degrees 28 minutes and 28 seconds. This means that we can rewrite the given expression as the tan of 71 degrees 28 minutes and 28 seconds all divided by two.

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