Question 69

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

Solution

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

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

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

= $$[\frac{cos(A - B)}{sin A sin B}] \div [\frac{sin(A - B)}{sin A sin B}]$$

= $$[\frac{cos(A - B)}{sin A sin B}] \times [\frac{sin A sin B}{sin(A - B)}]$$

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

=> Ans - (B)

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