Question

Find the exact value by using a half-angle identity. tan seven pi divided by eight

Answer 1

9514 1404 393

Answer:

  1 -√2

Step-by-step explanation:

  $\tan(x/2)=\dfrac{1-\cos(x)}{\sin(x)}\\\\\tan\left(\dfrac{1}{2}\cdot\dfrac{7\pi}{4}\right)=\dfrac{1-\cos\dfrac{7\pi}{4}}{\sin\dfrac{7\pi}{4}}=\dfrac{1-\dfrac{1}{\sqrt{2}}}{-\dfrac{1}{\sqrt{2}}}=\boxed{1-\sqrt{2}}$

tan(7π/8) = 1 -√2