Answer:
A. -3√7/7
Step-by-step explanation:
We have the equation in trigonometry as following:
with (cos x)^2 different from 0, we have:
[tex]\frac{1}{cos^{2}x } = 1 + tan^{2} x[/tex]
=> [tex]tan^{2} x = \frac{1}{cos^{2}x } -1[/tex]
As (cos θ) = √7/4 ≠ 0, so that we can replace θ into the above equation, we could have:
(tan θ)^2 = 1/[(cos θ)^2] -1
=> (tan θ)^2 = [tex]\frac{1}{(\sqrt{7}/4) ^{2} } -1 = \frac{1}{7/16} - 1[/tex]
=>(tan θ)^2 = 16/7 - 7/7 = 9/7
=> tan θ = (3√7)/7
or tan θ = - (3√7)/7
As θ is in quadrant IV, so that its tangent has negative value
=> tan θ = -3√7/7
So that the correct answer is A
