Question 55

If secA + tanA = x, then find the value of x.

Solution

Expression : sec A + tan A = x

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

Using, $$sin^2 A + cos^2 A = 1$$

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

= $$\frac{\sqrt{1 + sin A}}{\sqrt{1 - sin A}} = \sqrt{\frac{1 + sin A}{1 - sin A}}$$

=> Ans - (D)

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