Question

The value of $\cos^2 \, 45^{\circ} - \sin^2 \, 15^{\circ}$ is

• A. $\frac{\sqrt{3}}{2}$
• B. $\frac{\sqrt{3}}{4}$
• C. $\frac{\sqrt{3} + 1}{2 \sqrt{2}}$
• D. $\frac{\sqrt{3} - 1}{2 \sqrt{2}}$

Answer 1

Answer: (B)

$ \cos ^{2} 45^{\circ}-\sin ^{2} 15^{\circ} $
$= \cos \left(45^{\circ}+15^{\circ}\right) \cos \left(45^{\circ}-15^{\circ}\right)$
$\left[\because \cos ^{2} A-\sin ^{2} B=\cos (A+B) \cos (A-B)\right] $
$= \cos 60^{\circ} \cos 30^{\circ}=\frac{1}{2} \times \frac{\sqrt{3}}{2}=\frac{\sqrt{3}}{4} $