Respuesta :

First you must write the expression as 

1/(1 – Cos(x)) – 1/(1 + Cos(x)) = 2Csc(x)Cot(x) 

You may have read 1 – cosX as a denominator, but nobody else will. 

The common denominator of the left side is (1 – Cos(x))(1 + Cos(x)) 

So the left side is 

[(1 + Cos(x) – (1 – Cos(x))]/[(1 – Cos(x))(1 + Cos(x))] 

Which simplifies to 

[2Cos(x)]/[1 - Cos²(x))] = [2Cos(x)]/[Sin²(x)] 

= 2[Cos(x)/Sin(x)][1/Sin(x)] 

= 2Cot(x)Csc(x) as required 

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