How do you prove cotangent's difference formula

cot(alpha-beta)=cot(alpha)xcot(beta)/cot…

I would write cot(A-B)= cos(A-B)/sin(A-B)

= cosAcosB+ sinAsinB
-------------------------------
SinAcosB- cosAsinB

Divide each term by sinAsinB:

= (cosAcosB)/(sinAsinB) + (sinAsinB)/(sinAsinB)
--------------------------------------…
(sinAcosB)/(sinAsinB) - (cosAsinB)/(sinAsinB)

= (cotAcotB) + 1
-----------------------
CotB - cotA

I hope this helps!

Hint: cot(x) = 1 / tan(x)