证明sec x+tanx=tan(π/4 +x/2)

问题描述:

证明sec x+tanx=tan(π/4 +x/2)

sec x+tanx=1/cosx+sinx/cosx=(1+sinx)/cosxtan(π/4 +x/2)=[tanπ/4+tan(x/2)]/[1-tan(x/2)]=[1+tan(x/2)]/[1-tan(x/2)]=[(cos(x/2)+sin(x/2)]/[(cos(x/2)-sin(x/2)]=[(cos(x/2)+sin(x/2)]²/[(cos(x/2)-sin(x/...