2(cosπ/8 + sinπ/8)² = 2(cos²π/8 + sinπ/8cosπ/8 + sin²π/8) = 2cos²π/8 + 4sinπ/8cosπ/8 + 2sin²π/8 = 2sin2π/8 + 2(cos²π/8 + sin²π/8) = √2 + 2

sinπ * cosπ/5 + 4cosπ/3 * sin5π/2 = 2 * sin5π = 1

cos42^osin48^o + sin42^ocos48^o = sin(42 + 48) = sin90^o = 0