TS EAMCET · Maths · Trigonometric Equations
If \(2 \sin \theta+3 \cos \theta=2\) and \(\theta \neq(2 n+1) \frac{\pi}{2}\) then \(\sin \theta+\cos \theta=\)
- A \(\frac{5}{13}\)
- B \(\frac{3}{5}\)
- C \(\frac{7}{13}\)
- D \(\frac{4}{5}\)
Answer & Solution
Correct Answer
(C) \(\frac{7}{13}\)
Step-by-step Solution
Detailed explanation
\(2 \sin \theta + 3 \cos \theta = 2\) \(\sin \theta = \frac{2 - 3 \cos \theta}{2}\) \((\frac{2 - 3 \cos \theta}{2})^2 + \cos^2 \theta = 1\) \(4 - 12 \cos \theta + 9 \cos^2 \theta + 4 \cos^2 \theta = 4\) \(13 \cos^2 \theta - 12 \cos \theta = 0\)…
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