Question

Use a difference identity to find the exact value of tan 15.

Answer 1

X minus positive three minus -2 equals 7-15

Answer 2

`2-√(3)`

Explanation:

`tan15 = tan(45 - 30)=(tan(45)-tan(30))/(1+tan(45)tan(30))\\\\=(1-(1)/(√(3)))/(1+(1)/(√(3)))\\\\\\=(√(3)-1)/(√(3)+1)\\\\\\`

`=((√(3)-1)^2)/(3-1)\\=(3+1-2√(3))/(2)\\=2-√(3)`