cotx cot2x - cot2x cot3x-cot3x cotx=1

**Here's the easiest method.**

**Find out, what's the biggest angle here? It's "cot 3x"**

**cot (3x) = cot ( 2x+x )**

**Apply, cot (A+B) = (cot A.cot B -1)/ cot A + cot B**

**So,**

**cot (3x) = ( cot 2x.cot x - 1 ) / cot 2x + cot x**

**Now, cross multiply**

**cot 3x ( cot 2x + cot x ) = cot 2x.cot x - 1**

**cot 2x.cot 3x + cot x.cot 3x = cot 2x.cot x - 1**

**cot 2x.cot x - cot 2x.cot 3x - cot x.cot 3x = 1**

**This is by far the easiest method, I've came across.**

**This method is applicable for both tan and cot..! :) **

**Hope I helped..!! :D**

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