The value of (cosec A + cot A)(1 - cos A) is:

(cosec A + cot A)(1 - cos A)

= ( \(\frac{1}{sinA}\) + \(\frac{cos}{sinA}\))(1 - cos A)

= ( \(\frac{1 + cosA}{sinA}\) )(1 - cos A)

= ( \(\frac{1 - cos²A}{sinA}\) )

{ using , sin²A + cos²A = 1 }

= ( \(\frac{sin²A}{sinA}\) )

= sinA