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

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