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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2022 · Mathematics · Trigonometric Ratios & Identities

If x=(25)/(24) and x lies in the fourth quadrant, then what is the...

If sec⁡x=2524\sec x=\frac{25}{24} and xx lies in the fourth quadrant, then what is the value of tan⁡x+sin⁡x\tan x+\sin x ?

Options

  1. A−625168-\frac{625}{168}
  2. B−343600-\frac{343}{600}
  3. C625168\frac{625}{168}
  4. D343600\frac{343}{600}

Correct answer

B. −343600-\frac{343}{600}

Step-by-step solution

<br/><br/>sec⁡x=2524=hbP=(25)2−(24)2=7∴tan⁡x+sin⁡x=(−724)+(−725)=−7[124+125]=−343600\begin{aligned} & \sec x=\frac{25}{24}=\frac{h}{b} \\ & P=\sqrt{(25)^2-(24)^2}=7 \\ & \therefore \tan x+\sin x=\left(-\frac{7}{24}\right)+\left(-\frac{7}{25}\right) \\ & =-7\left[\frac{1}{24}+\frac{1}{25}\right]=\frac{-343}{600}\end{aligned}$$
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