Question

sinA+sin3A+sin5A=a,cosA+cos3A+cos5A=b,求证（2cos2A+1）平方=a平方+b平方

Answer 1

sinA+sin5A+sin3A = a => 2 sin3Acos2A + sin3A = a

cosA+cos5A+cos3A=b => 2 cos3Acos2A + cos3A = b

即 sin3A (2 cos2A + 1) = a,cos3A (2 cos2A + 1) = b,

∴ a² + b² = (2 cos2A + 1)²