If (cotAcotB - 1) / (cotB + cotA) = x, then the value of x is

Expression : (cotAcotB - 1) / (cotB + cotA) = x

= $$(\frac{cos A}{sin A} \frac{cos B}{sin B} - 1) \div (\frac{cos B}{sin B} + \frac{cos A}{sin A})$$

= $$(\frac{cos Acos B - sin Asin B}{sin Asin B}) \div (\frac{sin Acos B + cos Asin B}{sin Asin B})$$

= $$(\frac{cos (A + B)}{sin Asin B}) \div (\frac{sin (A + B)}{sin Asin B})$$

= $$(\frac{cos (A + B)}{sin Asin B}) \times (\frac{sin Asin B}{sin (A + B)})$$

= $$\frac{cos (A + B)}{sin (A + B)} = cot (A + B)$$

=> Ans - (C)