MATH SOLVE

5 months ago

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

Accepted Solution

A:

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

cos315=cos(-45)=β2/2, sin315=-β2/2

tan157.5=(1-β2/2)/(-β2/2)=(2-β2)/(-β2)=(2β2-2)/(-2)=1-β2

cos315=cos(-45)=β2/2, sin315=-β2/2

tan157.5=(1-β2/2)/(-β2/2)=(2-β2)/(-β2)=(2β2-2)/(-2)=1-β2