Question 59

If cosecA - cotA = x, then the value of x is

Solution

Expression : cosecA - cotA = x

= $$\frac{1}{sin A} - \frac{cos A}{sin A} = \frac{1 - cos A}{sin A}$$

Multiplying both numerator and denominator by $$(1 + cos A)$$

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

= $$\frac{1 - cos^2 A}{sin A(1 + cos A)} = \frac{sin^2 A}{sin A(1 + cos A)}$$

= $$\frac{sin A}{1 + cos A}$$

=> Ans - (C)

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