Use angle difference identity to find the exact value.

1. tan 15 degrees

2. tan - 105 degrees

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