Question

Упростите
cos36°+sin^2 18°

Answer 1

cos(2x) ≡ cos²(x) - sin²(x) 
тогда
cos(36°) = cos²(18°) - sin²(18°)
Исходное выражение = cos²(18°) - sin²(18°) + sin²(18°) = cos²(18°)

Answer 2

$cos36^\circ+sin^218^\circ =cos^218^\circ -sin^218^\circ +sin^218^\circ =\\\\=cos^218^\circ =\Big (\frac{\sqrt{5+\sqrt5}}{2\sqrt2}\Big )^2=\frac{5+\sqrt5}{8}$