The identity `(1 + csc x)/sec x - cot x = cos x` has to be proved.

`(1 + csc x)/sec x - cot x`

=> `(1 + 1/sin x)/(1/cos x) - (cos x)/(sin x)`

=> `(cos x + cos x/sin x) - (cos x)/(sin x)`

=> `cos x + cos x/sin x - (cos x)/(sin x)`

=> `cos x`

**This proves that **`(1 + csc x)/sec x - cot x = cos x`