ExamBro
ExamBro
TS EAMCET · Maths · Trigonometric Equations

If \(2 \sin \theta+3 \cos \theta=2\) and \(\theta \neq(2 n+1) \frac{\pi}{2}\) then \(\sin \theta+\cos \theta=\)

  1. A \(\frac{5}{13}\)
  2. B \(\frac{3}{5}\)
  3. C \(\frac{7}{13}\)
  4. D \(\frac{4}{5}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{7}{13}\)

Step-by-step Solution

Detailed explanation

\(2 \sin \theta + 3 \cos \theta = 2\) \(\sin \theta = \frac{2 - 3 \cos \theta}{2}\) \((\frac{2 - 3 \cos \theta}{2})^2 + \cos^2 \theta = 1\) \(4 - 12 \cos \theta + 9 \cos^2 \theta + 4 \cos^2 \theta = 4\) \(13 \cos^2 \theta - 12 \cos \theta = 0\)…