Question

已知tan(α+π/4)=1/7,则tanα=

Answer 1

tan(α+π/4)=[tanα+tan(π/4)]/[1-tanαtan(π/4)]=(tanα +1)/(1-tanα)=1/7
1-tanα=7(tanα+1)
1-tanα=7tanα+7
8tanα=-6
tanα=-3/4

Answer 2

由公式 cos2(α+π/4)=[1-tan²(α+π/4)]/[1+tan²(α+π/4)]=24/25
而 cos2(α+π/4)=cos(2α +π/2）=-sin2α
所以 sin2α=-24/25
从而 所求=24/25 /（1-24/25）=24