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Simplify $$\tan \frac{\pi}{24} + \tan \frac{7 \pi}{24}.$$

Sep 5, 2022

#1
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Before you start begging like some crazy dude, think about the problem.

Express those terms in the form of sine and cosine, then try to express these terms using half angle identities. If you're unable to do this, you may need to try easier problems and work your way up from there. :)

Sep 5, 2022
#2
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i got it thank you for the hint

pogfrog123456789  Sep 5, 2022
#3
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Yep, another way you could solve it is by noting that:

tan(8pi/24) = ( tan(pi/24) + tan (7pi/24) )/ ( 1 - tan(pi/24)tan (7pi/24) )

Express the tan's in terms of sine and cosine, and use the sum to product identities :)

Sep 5, 2022