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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