Question

已知tanα=t 用t表示sinαcosα,

Answer 1

tana =sina/cosa=t

平方

t^2 = (sina)^2/(cosa)^2

+1

t^2 +1= 1/(cosa)^2

所以,cosa = ±√[1/t^2 +1)]

再根据,sina=±√[1-(cosa)^2]有,

sina = ±√[t^2/(t^2 +1)]

所以,sinacosa = ±t/(t^2 +1)