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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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