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cot(15)=1/tan(15)

Let us find tan(15)

tan(15)=tan(45-30)

tan(a-b) = (tan(a)-tan(b))/(1+tan(a)tan(b))

tan(45-30)= (tan(45)-tan(30))/(1+tan(45)tan(30))

substitute tan(45)=1 and tan(30)=1/√3 into the equation.

tan(45-30) = (1- 1/√3) / (1+1/√3)

=(√3-1)/(√3+1)

The exact value of cot(15) is the reciprocal of the above which is:

(√3+1) /(√3-1)

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