## anonymous one year ago Find the exact value by using a half-angle identity. tangent of seven pi divided by eight.

1. mathstudent55

$$\large \tan \dfrac{7 \pi}{8} = \tan \dfrac{\frac{7 \pi}{4}}{2}$$

2. mathstudent55

$$\tan \dfrac{\theta}{2} = \dfrac{1 - \cos \theta}{\sin \theta}$$ $$\cos \dfrac{7\pi}{4}$$ and $$\sin \dfrac{7\pi}{4}$$ are well known.

3. anonymous

1-sqrt2