What is the exact value of tan(pi/24) in fractional form

Recall the half angle identities for sine and cosine:




So you have



This is useful because we have



Unfortunately, we need to know the value of to continue. But we can use either of the half-angle identities to figure this out.






where you take the positive root since is positive when .

So, you have





again taking the positive root because is positive when .

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