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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2019 · Mathematics · Trigonometric Ratios & Identities

If cosec θ=(29)/(21) where 0 < θ < 90^ ^ , then what is the value...

If cosec⁡θ=2921\operatorname{cosec} \theta=\frac{29}{21} where 0<θ<90∘0 < \theta < 90^{{}^{\circ}}, then what is the value of 4sec⁡θ+4tan⁡θ4 \sec \theta+4 \tan \theta ?

Options

  1. A5
  2. B10
  3. C15
  4. D20

Correct answer

B. 10

Step-by-step solution

Given: cosec⁡θ=2921=HP∵\operatorname{cosec} \theta=\frac{29}{21}=\frac{H}{P}\because we have Pythagorean triplet of (20,21,29)(20,21,29)∴P=21B=20H=29\begin{aligned} & \therefore \quad P=21 \\ & B=20 \\ & H=29 \end{aligned}$\begin{aligned} & \therefore 4(\sec \theta+\tan \theta)=4\left(\frac{29}{21}+\frac{21}{20}\right) \\ & \approx \frac{200}{20}=10\end{aligned}
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