求证:secx - tanx = tan(π/4 - x/2)
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求证:secx - tanx = tan(π/4 - x/2)
![求证:secx - tanx = tan(π/4 - x/2)](/uploads/image/z/15379763-59-3.jpg?t=%E6%B1%82%E8%AF%81%EF%BC%9Asecx+-+tanx+%3D+tan%28%CF%80%2F4+-+x%2F2%29)
secx-tanx=1/cosx-sinx/cosx=(1-sinx)/cosx
=(coxx/2-sinx/2)^2/(cosx/2)^2-(sinx/2)^2
=(coxx/2-sinx/2)/(coxx/2-sinx/2)
tan(π/4 - x/2)=(1-tanx/2)/(1+tanx/2)
=(coxx/2-sinx/2)/(coxx/2-sinx/2)
∴secx - tanx = tan(π/4 - x/2)
=(coxx/2-sinx/2)^2/(cosx/2)^2-(sinx/2)^2
=(coxx/2-sinx/2)/(coxx/2-sinx/2)
tan(π/4 - x/2)=(1-tanx/2)/(1+tanx/2)
=(coxx/2-sinx/2)/(coxx/2-sinx/2)
∴secx - tanx = tan(π/4 - x/2)
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