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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.

Example 2 If $A=cos^2\theta+sin^4\theta$, for all values of $\theta$, then prove that $\frac{3}{4}\le A\le1$.

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Example 3 Find the value of $\sqrt3cosec20°-sec20°$

Example 4 If θ lies in the second quadrant, then show that $\sqrt{\frac{1-sin\theta}{1+sin\theta}}+\sqrt{\frac{1+sin\theta}{1-sin\theta}}=-2sec\ \theta$