大师作文网求证:(1+sinA-cosA)/(1+sinA+cosA)=tan(A/2)
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求证:(1+sinA-cosA)/(1+sinA+cosA)=tan(A/2)
(1+sinA-cosA)/(1+sinA+cosA)
= [sinA +2(sinA/2)^2]/[sinA + 2(cosA/2)^2]
= [2sin(A/2)*cos(A/2)+2(sinA/2)^2]/[2sin(A/2)*cos(A/2)+2(cosA/2)^2]
= {2sin(A/2)[cos(A/2) + (sinA/2)]} /{2cos(A/2)[sin(A/2) +(cosA/2)]}
= tan(A/2)
= [sinA +2(sinA/2)^2]/[sinA + 2(cosA/2)^2]
= [2sin(A/2)*cos(A/2)+2(sinA/2)^2]/[2sin(A/2)*cos(A/2)+2(cosA/2)^2]
= {2sin(A/2)[cos(A/2) + (sinA/2)]} /{2cos(A/2)[sin(A/2) +(cosA/2)]}
= tan(A/2)
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