# How do you find Tan 22.5 using the half angle formula?

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Apr 1, 2017

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Find tan (22.5)

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Call tan (22.5) = tan t --> tan 2t = tan 45 = 1

Use trig identity:

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Solve this quadratic equation for tan t.

There are 2 real roots:

tan t = -b/2a +- d/2a = -2/1 + 2sqrt2/2 = - 1 +- sqrt2

Answer:

Since tan 22.5 is positive, then take the positive answer:

tan (22.5) = - 1 + sqrt2

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