SOLUTION: what is the exact value of tan 3pi/16

Question 386784: what is the exact value of tan 3pi/16
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Find the exact value of .
Recall the identity .
Then from this come
(1)-----> , and
(2)-----> . Let
From (2) we get .
From this we get . This has solutions
, using the quadratic formula.
Eliminate , because >0.
Then substitute this value into (1):
, letting .
Hence the quadratic equation .
The solutions to this equation are . Again eliminate the negative value. Hence , the exact value of .

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