Question

Use angle difference identity to find the exact value.

1. tan 15 degrees

2. tan -105 degrees

Answer 1

Hello,

1)
tan (a-b)=(tan a - tan b)/(1+tan a tan b)

15=45-30
tan 45°= (√2/2)/(√2/2)=1
tan 30°=(1/2)/(√3/2)=√3/3
tan (45°-30°)= (1-√3/3)/(1+1*√3/3)=(3-√3)/(3+√3)=(3-√3)²/6=2-√3

tan (-105°)=tan (75°)= tan (60°+15°)=(tan 60+tan15°)/(1-tan 60°*tan 15°)

tan 15°=2-√3
tan 60°=√3°
tan (-105°)=(√3+2-√3)/(1-√3*(2-√3))=2/(1-2√3+3)=1/(2-√3)=2+√3