Đáp án+Giải thích các bước giải:

`a) 3cos^4 \alpha + sin^4 \alpha`

`= 2 cos^4 \alpha + (cos^2 \alpha + sin^2 \alpha)^2 - 2(sin \alpha cos \alpha)^2`

`= 2 cos^4 \alpha + 1 - 2 . (1/2 sin 2\alpha)^2`

`= 1 + 2 cos^4 \alpha - 1/2 sin^2 2\alpha`

`= 1 + 2 . ( (1 + cos 2 \alpha)/2)^2 - 1/2 . (1 - cos 4 \alpha)/2`

`= 1 + (1 + 2 cos 2 \alpha + cos^2 2\alpha)/2 - (1 - cos 4\alpha)/4`

`= (4 +2 + 4 cos 2\alpha + 2 cos^2 2\alpha - 1 + cos4 \alpha)/4`

`= (5 + 4 cos 2\alpha + 2cos^2 2\alpha + 2cos^2 2\alpha - 1)/4`

`= (4 + 4 cos 2\alpha + 4 cos^2 2\alpha)/4`

`= 1 + cos 2\alpha + cos^2 2\alpha` (đpcm)

`b)` `A = 8sin^4 x + 4 cos 2x - cos 4x - 3`

`A = 8 . ( (1 - cos 2x)/2)^2 + 4 . cos 2x + 1 - 2cos^2 2x  - 3`

`A = 2(1 - 2cos2x + cos^2 2x) + 4 cos 2x - 2 - 2cos^2 2x`

`A = 2 - 4 cos 2x + 2 cos^2 2x + 4 cos 2x - 2 - 2cos^2 2x`

`A = 0`

`c)` `(1 + sin 6\alpha - cos 6 \alpha)/(1 + sin 6 \alpha + cos 6 \alpha)`

`= (2sin^2 3\alpha + 2 sin 3\alpha cos 3\alpha)/(2 cos^2 3\alpha + 2sin 3 \alpha cos 3 \alpha)`

`= (2sin 3 \alpha (sin 3\alpha + cos 3\alpha))/(2cos 3 \alpha (sin 3\alpha + cos 3\alpha))`

`= (sin 3\alpha)/(cos 3\alpha)`

`= tan 3\alpha` (đpcm)