Question 61

If cot(A + B) = x, then value of x is

Solution

Expression : cot(A + B) = x

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

= $$\frac{cosAcosB - sinAsinB}{sinAcosB + cosAsinB}$$

Dividing both numerator and denominator by $$(sinAsinB)$$, we get :

= $$\frac{cosAcosB - sinAsinB}{sinAsinB} \div \frac{sinAcosB + cosAsinB}{sinAsinB}$$

= $$(\frac{cosAcosB}{sinAsinB} - 1) \div (\frac{cosB}{sinB} + \frac{cosA}{sinA})$$

= $$\frac{cotAcotB - 1}{cotB + cotA}$$

=> Ans - (C)

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