Question: Determine the exact value of \( \tan \frac{\pi}{4} \)

Answer:

\(\tan 2 \theta = (2 \tan \theta)/(1- \tan² \theta)\)

\( \tan(π/6)=(2tan π/12)/(1-tan² π/12)\)

\(tanπ/12=t\)

\(1/√3=2t/(1-t²)\)

\(t²+2√3t-1=0\)

\(∆=(2√3)²+4=16\)

\(t=(-2√3±4)/2 =-√3±2\)

\(tan(π/12)=2-√3\)