计算 tanπ/12+1/tanπ/12
问题描述：
计算 tanπ/12+1/tanπ/12
答
tanπ/12+1/tanπ/12
=(sinπ/12)/(cosπ/12)+(cosπ/12)/(sinπ/12)
=(sin²π/12+cos²π/12)/(sinπ/12 * cosπ/12)
=2/(2*sinπ/12 * cos²π/12)
=2/(sinπ/6)
=4
答
公式：tan2α=2tanα/（1+tan²α）
所以 tanπ/12+1/tanπ/12
=[tan²（π/12）+1]/tan（π/12）
=2*{[tan²（π/12）+1]/[2tan（π/12）]}
=2*1/tan[2*（π/12）]
=2/tan（π/6）
=2√3