Use a half-angle identity to find the exact value of tan 157.5°.

Use the half angle identity, tan157.5=(1-cos315)/sin315
cos315=cos(-45)=√2/2, sin315=-√2/2
tan157.5=(1-√2/2)/(-√2/2)=(2-√2)/(-√2)=(2√2-2)/(-2)=1-√2