Question 944383
how to establish cot^2 x/2 = (sec x + 1) / (sec x -1) ?
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start with left side:
Identity:{{{tan(x/2)=sinx/(1+cosx)}}}
{{{cot(x/2)=(1+cosx)/sinx}}}
{{{cot^2(x/2)=(1+cosx)^2/sin^2(x)
=(1+cosx)^2/(1-cos^2(x))
=(1+cosx)^2/(1-cos^2(x))
=(1+cosx)^2/(1+cosx)(1-cosx)
=(1+cosx)/(1-cosx)=(1+(1/secx))/(1-(1/secx))=(secx+1)/(secx-1)}}}
verified: left side=right side