AP EAMCET · Maths · Trigonometric Equations
If \(0 \leq x \leq 3\) and \(0 \leq y \leq 3\), then the number of solutions \((x, y)\) of the equation \(\left(\sqrt{\sin ^2 x-\sin x+\frac{1}{2}}\right) 2^{\sec ^2 y}=1\) is
- A \(5\)
- B \(2\)
- C \(6\)
- D \(1\)
Answer & Solution
Correct Answer
(B) \(2\)
Step-by-step Solution
Detailed explanation
\(\sqrt{\sin ^2 x-\sin x+\frac{1}{2}} = \sqrt{(\sin x - \frac{1}{2})^2 + \frac{1}{4}} \geq \frac{1}{2}\) \(2^{\sec ^2 y} \geq 2^1 = 2\) (since \(\sec^2 y \geq 1\)) For the equation to hold, both factors must attain their minimum values:…
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