Question

The value of ${\sin }^2{75}^{\circ }-{\sin }^{2}15$ is

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

Answer 1

The correct option is C $\frac{3}{4}$

${\sin }^2{75}^{\circ }-{\sin }^2{15}^{\circ }$

$={\sin }^2({90}^{\circ }-{15}^{\circ })-{\sin }^2{15}^{\circ }$

$={\cos }^2{15}^{\circ }-{\sin }^2{15}^{\circ }$

$=\cos 2\times {15}^{\circ }$

$=\cos {30}^{\circ }$

$=\frac{\sqrt{3}}{2}$