AP EAMCET · Maths · Trigonometric Ratios & Identities
If \(\alpha\) is the maximum value and \(\beta\) is the minimum value of \(\cos ^2 \frac{x}{4}+\sin \frac{x}{4}\), \(x \in R\), then \(\alpha-\beta=\)
- A \(\frac{1}{4}\)
- B \(\frac{9}{4}\)
- C \(2\)
- D 3
Answer & Solution
Correct Answer
(B) \(\frac{9}{4}\)
Step-by-step Solution
Detailed explanation
Let \(y = \sin \frac{x}{4}\). Since \(x \in R\), \(y \in [-1, 1]\). The expression becomes \(f(y) = (1 - \sin^2 \frac{x}{4}) + \sin \frac{x}{4} = 1 - y^2 + y\). Consider \(g(y) = -y^2 + y + 1\) for \(y \in [-1, 1]\). The vertex of the parabola is at…
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\begin{array}{llll}
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The correct answer isAP EAMCET 2023 Easy - If the points with position vectors \((\alpha \hat{i}+10 \hat{j}+13 \hat{k})\), \((6 \hat{i}+11 \hat{j}+11 \hat{k}),\left(\frac{9}{2} \hat{i}+\beta \hat{j}-8 \hat{k}\right)\) are collinear then \((19 \alpha-6 \beta)^2=\)AP EAMCET 2024 Medium