`tanx-cotx=2`

`<=> (tanx-cotx)^2=4`

`<=> tan^2x-2tanx cotx+cot^2x=4`

`<=> tan^2x+cot^2x=6`

`<=> [sin^2x]/[cos^2x]+[cos^2x]/[sin^2x]=6`

`<=> [sin^4x+cos^4x]/[sin^2x cos^2x]=6`

`<=> sin^4x +cos^4x=6sin^2x cos^2x`

`<=> (sin^2x+cos^2x)^2-2sin^2x cos^2x=6(sin^2x cos^2x)`

`<=> 1-2sin^2x cos^2x=6sin^2x cos^2x`

`<=> 8sin^2x cos^2x=1`

`<=> sin^2x cos^2x=1/8`

Đề:

`P=1/[cos^2x sin^2x]+(tanx+cotx)^2`

`P=6/[sin^4x+cos^4x]+tan^2x+2+cot^2x`

`P=6/[sin^4x+cos^4x]+8`

`P=6/[(sin^2x+cos^2x)^2-2sin^2xcos^2x]+8`

`P=6/[1-2sin^2x cos^2x]+8`

`P=6/[1-2*1/8]+8`

`P=6/[1-1/4]+8`

`P=6/[3/4]+8`

`P=8+8`

`P=16`