Question

Find the exact value of

1. tan 75 degrees
2. Cos 15 degrees
3. Sin 105 degrees

Answer 1

you know the values for 30 and 45 degrees
use your sum/difference and half-angle formulas

75=45+30
15=30/2
105=90+15

Answer 2

Tan 75 = tan (45 +30)
= tan 45 + tan 30/1-tan 45 *tan 30
= (1+ 1/√3)/(1-1/√3) = √3 + 1/√3-1
= √3 + 1/√3-1 (afterationalization )
= 2+√3
cos 15 = cos (45 - 30)

= cos 45 cos 30+ sin 45 sin 30
=