ctg(13/12π)-ctg(5/12π)

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ctg(13/12π)-ctg(5/12π)ctg(13/12π)-ctg(5/12π)ctg(13/12π)-ctg(5/12π)ctg(13/12π)-ctg(5/12π)=ctg(π/12)-t

ctg(13/12π)-ctg(5/12π)
ctg(13/12π)-ctg(5/12π)

ctg(13/12π)-ctg(5/12π)
ctg(13/12π)-ctg(5/12π)
=ctg(π/12)-tg(π/12)
=cos(π/12)/sin(π/12)-sin(π/12)/cos(π/12)
=[cos²(π/12)-sin²(π/12)]/[sin(π/12)cos(π/12)]
=cos(π/6)/[1/2sin(π/6)]
=(√3/2)/(1/4)
=2√3