TS EAMCET · Maths · Trigonometric Ratios & Identities
If \(\theta\) lies in the first quadrant and \(5 \tan \theta=4\), then \(\frac{5 \sin \theta-3 \cos \theta}{\sin \theta+2 \cos \theta}\) is equal to
- A \(\frac{5}{14}\)
- B \(\frac{3}{14}\)
- C \(\frac{1}{14}\)
- D \(0\)
Answer & Solution
Correct Answer
(A) \(\frac{5}{14}\)
Step-by-step Solution
Detailed explanation
Given, \(\theta\) lies in the first quadrant \(\begin{array}{rlrl}\text { and } & 5 \tan \theta & =4 \\ \Rightarrow & \tan \theta & =\frac{4}{5} \\ & \therefore & \sin \theta=\frac{4}{\sqrt{41}}, \cos \theta & =\frac{5}{\sqrt{41}}\end{array}\) Now,…
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