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Đáp án: + Giải thích các bước giải:

`sin^2 \alpha + cos^2 \alpha = 1`.

`tan\alpha.cot\alpha=1`

`tan\alpha = {sin\alpha}/{cos\alpha}, cot\alpha = {cos\alpha}/{sin\alpha}`

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

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

`c. sin \alpha . cos \alpha(1+tan\alpha)(1+cot \alpha)`

`= sin\alpha . cos\alpha (1+tan\alpha+cot \alpha+tan\alpha.cot\alpha)`

`= sin\alpha . cos\alpha (2+{sin\alpha}/{cos\alpha}+{cos\alpha}/{sin\alpha})`

`= 2 sin\alpha . cos\alpha + sin^2\alpha + cos^2\alpha`

`= 1 + 2sin\alpha . cos\alpha`