Respuesta :
The one of the solution of trigonometric inequality
[tex]3-tan(x) \geq 4-2tan(x)[/tex] over the interval [tex]0 \leq x \leq 2\pi[/tex] radians is . [tex]x = \frac{\pi }{3}[/tex]
What is trigonometric inequality?
An inequality of the standard form R(x) > 0 (or < 0) that consists of 1 or a few trigonometric functions of the variable arc x is a trigonometric inequality. Finding a solution to the inequality means determining the values of the variable arc x whose trigonometric functions make the inequality true.
According to the question
The trigonometric inequality is :
[tex]3-tan(x) \geq 4-2tan(x)[/tex]
over the interval [tex]0 \leq x \leq 2\pi[/tex] radians
Now ,
Solving the trigonometric inequality
[tex]3-tan(x) \geq 4-2tan(x)[/tex]
[tex]2tan(x) - tan(x) \geq 4 - 3[/tex]
[tex]tan(x)\geq 1[/tex]
we know that
tan(45°) = 1
Therefore , substituting the value of tan(45°) at place of 1
[tex]tan(x)\geq tan(45)[/tex]
comparing both side
[tex]x\geq 45[/tex]
x in radian
[tex]x \geq \frac{\pi }{4}[/tex]
but the interval of x is 0 ≤ x ≤ 2[tex]\pi[/tex]
Now,
[tex]tan (x)[/tex] will be greater than 1 only when x lies between 45° or [tex]\frac{\pi }{4}[/tex] and 90 or π .
Hence, the one of the solution of trigonometric inequality
[tex]3-tan(x) \geq 4-2tan(x)[/tex] over the interval [tex]0 \leq x \leq 2\pi[/tex] radians is . [tex]x = \frac{\pi }{3}[/tex]
To know more about trigonometric inequality here:
https://brainly.com/question/20719017
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