Rút gọn `A=(sin^(4) alpha+cos^(4)alpha-1).(tan^(2)alpha+cot^(2)alpha+2)`

Đáp án:

 `-2.`

Giải thích các bước giải:

 `A=(sin^4 alpha+cos^4 alpha -1)(tan ^2 alpha+cot^2 alpha+2)`

`=>A=[(sin^2 alpha+cos^2 alpha)^2-2cos^2 alpha.sin^2 alpha -1].(tan ^2 alpha+2cot alpha.tan alpha+cot ^2 alpha)`

`=>A=(1-2cos^2 alpha sin ^2 alpha-1)(tan alpha+cot alpha)^2`

`=>A=-2cos^2 alpha.sin^2 alpha.((sin alpha)/cos alpha+cos alpha/ sin alpha)^2`

`=>A=-2cos^2 alpha.sin^2 alpha.((sin^2 alpha+cos^2 alpha)/(sin alpha.cos alpha))^2`

`=>A=-2.`

Vậy `A=-2.`

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