Question

HELP!! What is the exact value of Tangent (pi/12)

Answer 1

Answer: Option 4 or D) 1/2-sqrt3

Step-by-step explanation: EDGE 2021

Answer 2

Answer:

2 - sqrt(3)

Step-by-step explanation:

Split pi/12 into two angles where the values of the six trigonometric functions are known.

tan (pi/4 - pi/6)

Apply the difference of angles identity

$\frac{tan(pi/4) - tan(pi/6)}{1 + tan(pi/4)tan(pi/6)}$

tan(pi/4) = 1 , tan(pi/6) = (sqroot3)/3

Plug in and Simplify

$\frac{1-\frac{\sqrt{3} }{3} }{1+1\frac{\sqrt{3} }{3} }$

$\frac{\frac{3-\sqrt{3} }{3} }{\frac{3+\sqrt{3} }{3} }$

$\frac{3-\sqrt{3} }{3} *\frac{3}{3+\sqrt{3} }$

$\frac{3-\sqrt{3} }{3+\sqrt{3}}$ Need to multiply this by $\frac{3+\sqrt{3} }{3+\sqrt{3} }$

Expand and simplify numerator: $\frac{6}{(3+\sqrt{3} )^{2} }$

Expand and simplify denominator: $\frac{6}{12+6\sqrt{3}}$

Cancel the common factor: $\frac{1}{2+\sqrt{3}}$