ExamBro
ExamBro
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

  1. A \(\frac{5}{14}\)
  2. B \(\frac{3}{14}\)
  3. C \(\frac{1}{14}\)
  4. D \(0\)
Verified Solution

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,…