Giúp mình với ạ

Ta có: `sqrt(1+cosalpha)-sqrt(1-cosalpha)`

`=sqrt(2*(1+cosalpha)/2)-sqrt(2*(1-cosalpha)/2)`

`=sqrt(2*cos^2 \ alpha/2)-sqrt(2*sin^2 \ alpha/2)`

`=sqrt2abs(cos \ alpha/2) - sqrt2abs(sin \ alpha/2)`

Do `0 < alpha < pi, alpha ne pi/2` `=>` `0 < alpha/2 < pi/2`

`=>` `cos \ alpha/2, sin \ alpha/2 > 0`

`=>` `VT = sqrt2cos \ alpha/2-sqrt2sin \ alpha/2`

`=2*(sqrt2/2cos \ alpha/2-sqrt2/2sin\alpha/2)`

`=2*(cos \ alpha/2cos \ pi/4 - sin \ alpha/2sin \ pi/4)`

`=2cos(alpha/2+pi/4)`

Thêm vào đó, `sqrt(1+cosalpha)+sqrt(1-cosalpha)=2sin(alpha/2+pi/4)` với `0 < alpha < pi, alpha ne pi/2`

`=>` `(sqrt(1+cosalpha)+sqrt(1-cosalpha))/(sqrt(1+cosalpha)-sqrt(1-cosalpha))=(2sin(alpha/2+pi/4))/(2cos(alpha/2+pi/4))=tan(alpha/2+pi/4)` (đpcm)