AP EAMCET · Maths · Trigonometric Equations
For \(\theta \in\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]\) if \(2 \cos \theta+\sin \theta=1\), and \(7 \cos \theta+6 \sin \theta=\mathrm{k}\), then the possible values of k are
- A \(8,-2\)
- B 6,2
- C 12,4
- D 7,6
Answer & Solution
Correct Answer
(B) 6,2
Step-by-step Solution
Detailed explanation
\(\sin \theta = 1 - 2 \cos \theta\) \(\cos^2 \theta + (1 - 2 \cos \theta)^2 = 1\) \(5 \cos^2 \theta - 4 \cos \theta = 0\) \(\cos \theta (5 \cos \theta - 4) = 0\) \(\cos \theta = 0\) or \(\cos \theta = \frac{4}{5}\) If \(\cos \theta = 0\), then \(\sin \theta = 1 - 2(0) = 1\)…
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