Cho tam giác ABC. Chứng minh có cosa/2.cosb/2.cosc/2 = sina/2.sinb/2.cosc/2 + sina/2.cosc/2.sinc/2 + cosa/2.sinb/2.sinc/2 =1/2

Ta có: A+B+C2=180°2=90°⇒cosA2+B2+C2=cos90°=0

⇔ cosA2+B2+C2=0 

⇔ cosA2+B2.cosC2−sinA2+B2.sinC2=0

⇔ cosA2.cosB2+sinA2.sinB2.cosC2−sinA2.cosB2+cosA2.sinB2.sinC2=0

⇔ cosA2.cosB2.cosC2−sinA2.sinB2.cosC2−sinA2.cosB2.sinC2−cosA2.sinB2.sinC2=0

⇔ cosA2.cosB2.cosC2=sinA2.sinB2.cosC2+sinA2.cosB2.sinC2+cosA2.sinB2.sinC2