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Đáp án + Giải thích các bước giải:

`a)` `P = 2(sin^6\alpha + cos^6\alpha) - 3(sin^4\alpha + cos^4\alpha)`

`=2(sin^2\alpha + cos^2\alpha)(sin^4\alpha - sin^2\alpha.cos^2\alpha + cos^4\alpha)- 3(sin^4\alpha + cos^4\alpha)`

`= 2(sin^4\alpha - sin^2\alpha.cos^2\alpha + cos^4\alpha)- 3(sin^4\alpha + cos^4\alpha)`

`= -sin^4\alpha - 2sin^2\alpha.cos^2\alpha - cos^4\alpha`

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

`= - (sin^2\alpha  + cos^2\alpha)^2`

`=-1`

`---------------`

`b)` Ta có:

`Q= \frac{2}{tan\alpha-1} + \frac{cot\alpha+1}{cot\alpha-1}`

`=\frac{2}{sin\alpha/cos\alpha - 1} + \frac{cos\alpha/sin\alpha + 1}{ cos\alpha/sin\alpha - 1}`

 `= \frac{2cos\alpha}{sin\alpha-cos\alpha} + \frac{sin\alpha+cos\alpha}{sin\alpha} . \frac{sin\alpha}{cos\alpha-sin\alpha}`

`= \frac{2cos\alpha}{sin\alpha-cos\alpha} - \frac{sin\alpha+cos\alpha}{sin\alpha-cos\alpha}`

`= \frac{2cos\alpha - sin\alpha-cos\alpha}{sin\alpha-cos\alpha}`

`= \frac{cos\alpha - sin\alpha}{sin\alpha-cos\alpha}`

`=-1`

`a)P=2(sin^6\alpha+cos^6\alpha)-3(sin^4\alpha+cos^4\alpha)`

`P=2(1-3/4sin^2\alpha)-3(1-1/2sin^2\alpha)`

`P=2-3/2sin^2\alpha-3+3/2sin^2\alpha`

`P=-1`

`->`đpcm

`b)Q=2/(tan\alpha-1)+(cot\alpha+1)/(cot\alpha-1)`

`Q=(2(cot\alpha-1)+(cot\alpha+1)(tan\alpha-1))/((tan\alpha-1)(cot\alpha-1))`

`Q=(2cot\alpha-2+1-cot\alpha+tan\alpha-1)/(1-tan\alpha-cot\alpha+1)`

`Q=(tan\alpha+cot\alpha-2)/(-tan\alpha-cot\alpha+2)`

`Q=(tan\alpha+cot\alpha-2)/(-(tan\alpha+cot\alpha-2))`

`Q=-1`

`->`đpcm