高中問題 求解

2012-10-19 3:21 am
設A為銳角,若sinA - cosA=1/根號2,求sinA+cosA=?

回答 (2)

2012-10-19 4:16 am
✔ 最佳答案
sinA - cosA=1/根號2

(sinA - cosA)^2=1/2

(sinA)^2+(cosA)^2-2*sinA*cosA=1/2

1/2=2*sinA*cosA

求sinA+cosA=?

(sinA+cosA)^2=(sinA)^2+(cosA)^2+2*sinA*cosA
=1+1/2=3/2

sinA+cosA=(根號6)/2
2012-10-19 4:35 am
設p=SinA+CosA>0
(SinA-CosA)^2+(SinA+CosA)^2=(1/√2)^2+p^2
2=(1/2)+p^2
p^2=3/2=6/4
p=√6/2


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