化简1+tanα×tan(α/2)

问题描述:

化简1+tanα×tan(α/2)

1+tanα×tan(α/2)
= (cosαcos(α/2) + sinαsin(α/2))/cosαcos(α/2)
= (cos(α-α/2))/cosαcos(α/2)
= cos(α/2)/cosαcos(α/2)
= 1/cosα