Question

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

Answer 1

Answer:

$2-\sqrt{3}$

Step-by-step explanation:

$tan15 = tan(45 - 30)=\frac{\tan{45}-\tan{30}}{1+\tan{45}\tan{30}}\\\\=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}\\\\\\=\frac{\sqrt{3}-1}{\sqrt{3}+1}$

$=\frac{(\sqrt{3}-1)^2}{3-1}\\=\frac{3+1-2\sqrt{3}}{2}\\=2-\sqrt{3}$

Answer 2

X minus positive three minus -2 equals 7-15