InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
If sec θ = \(\frac{13}{5}\), then what is the value of \(\frac{\text{2 sin θ - 3 cos θ}}{\text{4 sin θ - 9 cos θ}}\)?(a) 1 (b) 3 (c) 2 (d) 4 |
|
Answer» (b) 3 Given, sec θ = \(\frac{13}{5}\) ⇒ sec2 θ = \(\frac{169}{25}\) ⇒ 1 + tan2θ = \(\frac{169}{25}\) (∵ sec2θ – tan2θ = 1) ⇒ tan2 θ = \(\frac{169}{25}\) - 1 = \(\frac{144}{25}\) ⇒ tan θ = \(\frac{12}{5}\) ∴ \(\frac{2\,sin\,\theta-3\,cos\,\theta}{4\,\sin\,\theta-9\,cos\,\theta}\) = \(\frac{\frac{2\,sin\,\theta}{cos\,\theta}-3}{\frac{4\,sin\,\theta}{cos\,\theta}-9}\) (On dividing each term of numerator and denominator by cos θ) \(= \frac{2\,tan\,\theta-3}{4\,tan\,\theta-9}=\frac{2\times\frac{12}{5}-3}{4\times\frac{12}{5}-9}\) = \(\frac{24-15}{48-45}=\frac93=3.\) |
|