Question 55

If 2secA - (1 + sinA)/cosA = x, then the value of x is

Solution

Expression : 2secA - (1 + sinA)/cosA = x

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

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

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

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

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

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

=> Ans - (B)

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