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)

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