`=>` Tặng bạn
Đặt `P = sinA/2.sinB/2.sinC/2`.
`<=> 2P = ((2sinA)/2*(2.sinB)/2).(2sinC)/2 `
`<=> 2P = [cos(A/2-B/2) - cos(A/2+B/2)].sin(C/2) `
`<=> 2P = [cos(A/2-B/2) - sin(C/2)].sin(C/2)` `<=> 2P= sin(C/2).cos(A/2-B/2) - sin²(C/2)`
`<=> 8P = 4sin(C/2).cos(A/2-B/2) - 4sin²(C/2)`
`<=> 1-8P = 4sin²(C/2) - 4sin(C/2).cos(A/2-B/2) + cos²(A/2-B/2) + 1 - cos²(A/2-B/2) `
`<=> 1-8P = [2sin(C/2) - cos(A/2-B/2)]² + sin²(A/2-B/2) ≥ 0 (*) `
`=> P ≤ 1/8`
