The value of the tangent of angle 2x will be 2√8 / 7. Then the correct option is D.
What is trigonometry?
The connection between the lengths and angles of a triangular shape is the subject of trigonometry.
The trigonometric equation is given below.
cos x = –1/3
Then the sin x will be given as,
sin x = √(1 – cos² x)
sin x = √(1 – (–1/3)²)
sin x = 2√2 / 3
Then the value of tan x will be,
tan x = sin x / cos x
tan x = –2√2 / 1
tan x = 2√2
Then the value of tangent of angle 2x will be
[tex]\tan 2x = \dfrac{2 \tan x}{1 - \tan ^2 x}\\\\\tan 2x = \dfrac{2 (-2\sqrt 2)}{1 - (-2\sqrt 2) ^2 }\\\\\tan 2x = \dfrac{-4\sqrt 2}{1 - 8 }\\\\\tan 2x = \dfrac{-4\sqrt 2)}{-7}\\\\\tan 2x = \dfrac{2\sqrt 8)}{7}[/tex]
Thus, the value of the tangent of angle 2x will be 2√8 / 7.
Then the correct option is D.
More about the trigonometry link is given below.
https://brainly.com/question/22698523
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