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

Explanation:

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

tan(7π/8) = 1 -√2