Упростите. [latex] ( \frac{sin16}{2 cos^{2} 4-2 sin^{2} 4} )^{2} + 4 sin^{2} 41 cos^{2}41[/latex]

[latex]( \frac{sin16}{2 cos^{2} 4-2 sin^{2} 4} )^{2} + 4 sin^{2} 41 cos^{2}41=( \frac{sin16}{2(cos^{2} 4- sin^{2} 4)} )^{2} + (2 sin 41 cos41)^2= \\ \\ =( \frac{2sin8cos8}{2cos8} )^{2} + (2 sin 41 cos41)^2= sin^28+sin^282=sin^8+cos^28=1 [/latex]