Question

If $\sec \, \theta = x + \frac{1}{4x}, x \in R , x \neq 0$, then the value of $\sec \, \theta + \tan \, \theta$ is

• A. 2x
• B. $\frac{1}{2x}$
• C. $2x$ or $\frac{1}{2x}$
• D. none of these

Answer 1

Answer: (C)

$2x$ or $\frac{1}{2x}$

Answer 2

$\tan^{2} \theta = \sec^{2} \theta - 1$ $= \left(x+ \frac{1}{4x}\right)^{2} - 1 = \left(x - \frac{1}{4x}\right) ^{2}$ $\Rightarrow \tan\theta = \pm \left(x - \frac{1}{4x}\right)$ $\Rightarrow \sec\theta +\tan\theta = x + \frac{1}{4x} \pm\left( x - \frac{1}{4x}\right)$