Question

Find m if the following equation holds true ${\sin }^2{\left(52\frac{1}{2}\right)}^0-{\sin }^2{\left(22\frac{1}{2}\right)}^0=\frac{\sqrt{3}+1}{m\sqrt{2}}$

Answer 1

${\sin }^{2}52{\frac{1}{2}}^{\circ }-{\sin }^{2}22{\frac{1}{2}}^{\circ }=\sin (52{\frac{1}{2}}^{\circ }+22{\frac{1}{2}}^{\circ })\sin (52{\frac{1}{2}}^{\circ }-22{\frac{1}{2}}^{\circ })$

$=\sin {75}^{\circ }\sin {30}^{\circ }$

$=\frac{1}{2}\sin ({45}^{\circ }+{30}^{\circ })$

$=\frac{\sqrt{3}+1}{4\sqrt{2}}$

So $m=4$

The correct answer is $4$