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  4. If sec θ = x + (1/4x), x ∈ R , x ≠ 0, then the value of sec θ + tan θ is

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

Trigonometric Functions

Solution:

$\tan^{2} \theta = \sec^{2} \theta - 1$
$ = \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)$