Answer:
[tex]2-\sqrt{3}[/tex]
Step-by-step explanation:
Find the exact value of the expression, tan(15°).
The method I am about to show you will allow you to solve this problem without any tables or calculators. Although, memorizing the unit circle and trigonometric identities is required.
[tex]\tan(15 \textdegree)\\\\\Longrightarrow \tan(\frac{30 \textdegree}{2} )\\\\\text{Use the half-angle identity:} \ \tan(\frac{A}{2})=\pm \sqrt{\frac{1-\cos(A)}{1+\cos(A)} }=\frac{\sin(A)}{1+\cos(A)} =\frac{1-\cos(A)}{\sin(A)} \\\\\Longrightarrow\frac{1-\cos(30 \textdegree)}{\sin(30 \textdegree)} \\\\\text{From the unit circle:} \ \cos(30 \textdegree)=\frac{\sqrt{3} }{2} \ \text{and} \ \sin(30 \textdegree)=\frac{1}{2}\\[/tex]
[tex]\Longrightarrow \frac{1-\frac{\sqrt{3} }{2}}{\frac{1}{2}}\\\\\Longrightarrow 2(1-\frac{\sqrt{3} }{2})\\\\\therefore \boxed{\boxed{\tan(15 \textdegree)=2-\sqrt{3} }}[/tex]
Thus, the problem is solved.
