Question

Show all work! Use half angle to find the exact value of tan 15º

Answer 1

Answer:

0.2679

Step-by-step explanation:

Knowing that tg 45⁰ = 1, tg 30⁰= $1/\sqrt{3}$, and tg (a-b) = $\frac{tg a - tg b}{1+tg a. tg b}$ we have: tg 15⁰ = tg (45⁰-30⁰) = (tg 45⁰-tg 30⁰) / (1+tg 45⁰. tg 30⁰) = $\frac{1-1/\sqrt{3} }{1+1/\sqrt{3} } = \frac{\frac{\sqrt{3}-1 }{\sqrt{3} } }{\frac{\sqrt{3}+1 }{\sqrt{3} } } = \frac{\sqrt{3}-1 }{\sqrt{3}+1 }$ = 0.73205/2.73205 = 0.26794