Question

Тригонометрия. Вычислить если a =

Answer 1

$a^2=\frac{2+\sqrt{2+2cos(164^{\circ})}}{1+sin(8^{\circ})} \\cos(164^{\circ})=cos(180^{\circ}-16^{\circ})=-cos(16^{\circ})\\a^2=\frac{2+\sqrt{2-2cos(16^{\circ})}}{1+sin(8^{\circ})}\\2-2cos(16^{\circ})=2-2cos(2*8^{\circ})=2-2(1-2sin^2(8^{\circ}))=\\=2-2+4sin^2(8^{\circ})=4sin^2(8^{\circ})\\a^2=\frac{2+2sin(8^{\circ})}{1+sin(8^{\circ})} =2*\frac{1+sin(8^{\circ})}{1+sin(8^{\circ})} =2\\8a^2=8*2=16$

Ответ: 16