What is the value of tan((7pi)/8) ?

The value of tan((7pi)/8) is -sqrt(3-2\sqrt{2)}

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tan((7pi)/8)

tan (\frac{7 π}{8})

- 3 - 22

Solution steps

tan (\frac{7 π}{8})

Rewrite using trig identities:

- \frac{1 - cos ( \frac{7 π}{4} )}{1 + cos ( \frac{7 π}{4} )}

= - \frac{1 - cos ( \frac{7 π}{4} )}{1 + cos ( \frac{7 π}{4} )}

Rewrite using trig identities:

cos (\frac{7 π}{4}) = \frac{2}{2}

= - \frac{1 - \frac{2}{2}}{1 + \frac{2}{2}}

Simplify

- \frac{1 - \frac{2}{2}}{1 + \frac{2}{2}} : - 3 - 22

= - 3 - 22

2 cos (θ) - 2 = 0

tan (1 5^{\circ})

tan (θ) = 0

cos (10 5^{\circ})

2 sin^{2} (x) - 1 = 0

What is the value of tan((7pi)/8) ?
The value of tan((7pi)/8) is -sqrt(3-2\sqrt{2)}