Question 57

If 1 + secA = x, then the value of x is

Solution

Expression : 1 + secA = x

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

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

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

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

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

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

=> Ans - (C)

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