The identity `(sin A - cos A) (tan A + cot A) = sec A - cosec A` has to be proved.

`(sin A - cos A) (tan A + cot A)`

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

=> `(sin A - cos A) (sin A^2A + cos^2A)/(cos A*sin A)`

=> `(sin A - cos A)/(cos A*sin A)`

=> `1/cos A - 1/sin A`

=> `sec A - cosec A`

**This proves that **`(sin A - cos A) (tan A + cot A) = sec A - cosec A`

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