Question

$\sqrt{{\sin }^{4}x+4{\cos }^{2}x}-\sqrt{{\cos }^{4}x+4{\sin }^{2}x}=\cos sx$ Find s

Answer 1

The given expression is equal to
$\sqrt{{\sin }^{4}x+4(1-{\sin }^{2}x)}-\sqrt{{\cos }^{4}x+4(1-{\cos }^{2}x)}$
$=\sqrt{{(2-{\sin }^{2}x)}^2}-\sqrt{{(2-{\cos }^{2}x)}^2}$
$=(2-{\sin }^{2}x)-(2-{\cos }^{2}x)$
$={\cos }^{2}x-{\sin }^{2}x=\cos 2x$
Ans: 2