Question

If sec theta is equal to x + 1 by 4 x find sec theta + cos theta

Answer 1

Step-by-step explanation:

$sec \theta = \frac{x + 1}{4x}$

now required

$sec \theta + cos \theta = sec \theta + \frac{1}{ sec \theta} \\ \frac{x + 1}{4x} + \frac{4x}{x + 1} \\ = \frac{(x + 1) ^{2} + (4x)^{2} }{(4x)(x + 1)} \\ = \frac{( {x}^{2} + 1 + 2x) + (16 {x}^{2} }{4 {x}^{2} + 4x} \\ = \frac{17 {x}^{2} + 2x + 1}{4 {x}^{2} + 4x }$