Find the exact value using the half angle identify? #tan(7π/8)#

1 Answer
Dean R.
May 8, 2018

#tan ({7pi}/8) = 1 - sqrt{2} #

Explanation:

The usual form of the tangent half angle formula is the jarring

#tan( alpha/2) = sin (alpha) / {1 + cos (alpha) }#

#tan ({7pi}/8) = tan( (7pi//4)/2 ) = sin({7pi}/4)/{1 + cos ({7 pi}/4)} #

#tan ({7pi}/8) = {-1/sqrt{2}}/{1 + 1/sqrt{2}} = 1 - sqrt{2} #

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