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How do you simplify (secx-1)/tanx to tan(x/2) ??
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secx=1/cosx, tanx=sinx/cosx so we have ((1/cosx)-1)/(sinx/cosx)=(1-cosx)/(sinx) Now, 1-cosx=2sin^2(x/2) and sinx=2sin(x/2)cos(x/2) So, 2sin^2(x/2)/(2sin(x/2)cos(x/2))=sin(x/2)/cos(x/2)=tan(x/2)
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