Đáp án`+`Giải thích các bước giải:

`c,` Ta có: `cos^2 A + cos^2 B + cos^2 C`

`= (1 + cos 2A)/2 + (1 + cos 2B)/2 + (1 + cos 2C)/2`

`=3/2 + 1/2 (cos 2A + cos 2B + cos 2C)`

`= 3/2 + 1/2 [2cos (A+ B) cos(A - B) + cos 2C]`

`=3/2 + 1/2 [2cos (180^o - \hatC)  cos (A-B) + cos 2C]`

`= 3/2 +1/2 [- 2cosC cos(A- B) + cos 2C]`

`= 3/2 + 1/2 [-2cosC cos (A - B) + 2 cos^2 C - 1]`

`= 3/2 +1 /2 {- 2cosC [cos (A-B) - cosC] - 1}`

`= 3/2 + 1/2 {- 2cosC [cos (A-B) - cos(180^o - \hatA- \hatB)] - 1}`

`= 3/2+1/2 {-2 cosC [cos (A- B) + cos(A + B)] -1}`

`= 3/2 + 1/2 (- 2cosC . 2 cosA cosB - 1)`

`= 3/2 +1/2 (-4 cosA cosB cos C - 1)`

`= 3/2 - 2 cosA cosB cos C -1/2`

`= 1 - 2 cos A cos B cos C` (đpcm)

`***`sharksosad