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I NEED HELP WITH THIS QUESTION PLEASE, i don't have much time T^T

i'll give brainliest and points, thank you in advancee <33

an explanation for future reference would be appreciated!!^^​

I NEED HELP WITH THIS QUESTION PLEASE i dont have much time TT ill give brainliest and points thank you in advancee lt33an explanation for future reference woul class=

Respuesta :

Hrishii

Answer:

Option b is the correct answer

Step-by-step explanation:

  • [tex]\cos x = -\frac{12}{13}[/tex] (Given)

  • Formula relating sin x and cos x is given as below:

  • [tex]\sin^2x = 1-\cos^2x[/tex]

  • [tex]\implies \sin^2x = 1-\bigg(-\frac{12}{13}\bigg)^2[/tex]

  • [tex]\implies \sin^2x = 1-\frac{144}{169}[/tex]

  • [tex]\implies \sin^2x = \frac{169-144}{169}[/tex]

  • [tex]\implies \sin^2x = \frac{25}{169}[/tex]

  • [tex]\implies \sin x =\pm\sqrt{ \frac{25}{169}}[/tex]

  • [tex]\implies \sin x =\pm \frac{5}{13}[/tex]

  • It is given that: 180° < x < 270°. This means x falls in the third quadrant. In third quadrant sin ratio is negative.

  • [tex]\implies \sin x =- \frac{5}{13}[/tex]

  • Now, we will find the value of tanx by dividing sinx by cosx.

  • [tex]\implies \tan x =\frac{\sin x}{\cos x}[/tex]

  • [tex]\implies \tan x = \frac{-5/13}{-12/13}[/tex]

  • [tex]\implies\red{\bold{ \tan x =\frac{5}{12}}}[/tex]

  • tan (90° + x) and tan x both lie in the interval 180° < x < 270°. So, the values of both will be equal.

  • [tex]\implies \tan (90\degree + x ) =\tan x[/tex]

  • [tex]\implies \huge{\purple{\tan (90\degree + x ) =\frac{5}{12}}}[/tex]

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