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“The distance between insanity and genius is measured only by success.” —Bruce Feirstein

Example 1 A circular wire of radius 3 cm is cut and bent so as to lie along the circumference of a hoop whose radius is 48 cm. Find the angle in degrees which is subtended at the center of hoop.

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Example 2 If \( A=\cos^2\theta+\sin^4\theta\), for all values of \(\theta\), then prove that \(\frac{3}{4}\le A\le 1\).

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