Bài `1:`

Có : `cos^2 \alpha = 1-sin^2 \alpha = 1-9/25 = 16/25`

`-> cos \alpha = ± 4/5`

Mà `0<\alpha<pi/2`

`-> cos \alpha >0`

`-> cos \alpha=4/5`

`-> tan \alpha = (sin \alpha)/(cos\alpha) = (3/5)/(4/5) = 3/4`

`-> cot \alpha = 4/3`

`**) sin(\alpha + 7pi) = sin \alpha . cos 7pi +cos \alpha . sin 7pi`

`=3/5 . (-1) + 4/5.0`

`=-3/5`

Hoặc : `sin(\alpha + 7pi) = -sin \alpha = -3/5`

`**) cot (-\alpha) = -cot\alpha = -4/3`

Bài `2:`

`tan x = \sqrt{2} -> cot x = 1/\sqrt{2}`

Có : `1+tan^2 x = 1/(cos^2 x)`

`-> cos^2 x = 1/(1+tan^2 x)`

`= 1/3`

`-> cos x = ±1/\sqrt{3}`

Mà `180^o <x<270^o`

`-> cos x < 0`

`-> cos x = -1/\sqrt{3}`

Lại có :`tan x = (sin x)/(cos x)`

`-> sin x = tan x . cos x = \sqrt{2}.(-1)/\sqrt{3} = -\sqrt{2}/\sqrt{3}`

`**) cos (x+18pi) = cos x.cos 18pi - sin x.sin18pi`

`=-1\sqrt{3}.1+\sqrt{2}/\sqrt{3}.0`

`=-1/\sqrt{3}`

Hoặc : `cos (x+18pi) = cos x = -1/\sqrt{3}`

`**) cot(pi/2 -x) = tan x = \sqrt{2}`