Question

tan(∏/8)=

• A. 1-√2
• B. √2-1
• C. √2+1
• D. √2

Answer 1

Answer:

B. √2-1

$tan(\frac{∏}{4})=1$

$tan2x=\frac{2tanx}{1-tan^2x}$

$x=∏/8$

$tan(2\times \frac{∏}{8})=\frac{2tan\frac{∏}{8}}{1-tan^2\frac{∏}{8}}$

$1=\frac{2tan\frac{∏}{8}}{1-tan^2\frac{∏}{8}}$

${1-tan^2\frac{∏}{8}}=2tan\frac{∏}{8}$

$tan^2\frac{∏}{8}+2tan\frac{∏}{8}-1=0$

$x^2+2x-1=0$

$x=\frac{-2±\sqrt{4+4}}{2}=\frac{-2±2\sqrt2}{2}$

$x=-1±\sqrt2$

∏/8 in first quadtrant therefore +ve

tan(∏/8)=-1+√2=√2-1