Question

если cos15°-sin15°=
$frac{ alpha }{4 cos(15) }$
,то найдите A.
там это 4cos15°

Answer 1

$cos15^{circ}-sin15^{circ}=frac{alpha}{4cos15^{circ}} \ \ alpha =4cos15^{circ}(cos15^{circ}-sin15^{circ})=2cdot(2cos^2 15^{circ}-2sin15^{circ}cos15^{circ})=\\=2cdot(1+cos(2cdot15^{circ})-sin(2cdot15^{circ}))=2cdot(1+cos30^{circ}-sin30^{circ})=\\=2cdot(1+frac{sqrt{3}}{2}-frac{1}{2})=2cdot(frac{1}{2}+frac{sqrt{3}}{2})=1+sqrt{3}$