Question

tanα=sin2α/(1+cos2α)=(1-cos2α)/sin2α怎么得出tanα=(1+sin2α-cos2α)

Answer 1

sin2α = (1+cos2α) * tanα

1-cos2α = sin2α * tanα

两式相加：

sin2α + 1-cos2α = (1+cos2α + sin2α) * tanα (把公因式tanα提出)

所以tanα=(1+sin2α-cos2α)/(1+sin2α+cos2α)

其实这算是一个定理：k = a/b = c/d, 那么对于任意x, y, 只要bx+dy非零, 那么则有ax+cy/bx+dy = k