Question : What is the value of $\cos ^2 15°?$
Option 1: $(2+\sqrt{3})$
Option 2: $\frac{(2+\sqrt{3})}{4}$
Option 3: $\frac{(2+\sqrt{3})}{2}$
Option 4: $\frac{(1+\sqrt{3})}{2}$
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Correct Answer: $\frac{(2+\sqrt{3})}{4}$
Solution : According to the formula, $\cos 2A = 2\cos^2 A - 1$ Let A = 15° ⇒ $\cos 30° = 2\cos^2 15° - 1$ ⇒ $\cos^2 15° = \frac{\cos 30°+1}{2}$ ⇒ $\cos^2 15° = \frac{\frac{\sqrt3}{2}+1}{2}$ $\therefore\cos^2 15°=\frac{\sqrt3 + 2}{4}$ Hence, the correct answer is $\frac{2+\sqrt3}{4}$.
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