How do you solve cot5pi12 using sum and difference identityS

How do you solve cot(5pi/12) using sum and difference identity?

Solution

cot(5pi/12)

= cot((2pi/12)+(3pi/12))

= cot((pi/6)+(pi/4))

Cot (A+B) = (CotACotB-1)_{/(CotA + CotB)}

= (Cot(pi/6)Cot(pi/4)-1)_{/(Cot(pi/6)+ Cot(pi/4))}

= ((3)(1)-1)_{/(3 + 1)}

= (3 -1)_{/(3 + 1)}

cot(5pi/12) = (3 -1)_{/(3 + 1)}

cot(5pi/12) =0.267949