1/(1-tan π/8) - 1/(1+tan π/8) =多少?

题目

1/(1-tan π/8) - 1/(1+tan π/8) =多少?
1/(1-tan π/8) - 1/(1+tan π/8) =多少?

答案

令 x =tan π/8,
则 原式=1 /(1 -x) -1 /(1 +x)
= 2x /(1 -x^2)
=tan (2 *π/8)
=tan (π/4)
=1.
= = = = = = = = =
换元法.
倍角公式.
注意：
由 tan (A+B) =(tan A +tan B) / [ 1 -(tan A)(tan B) ],
得到 tan 2A =2tan A /[ 1 -(tan A)^2 ].
分母是减.