Question

Chứng minh các đằng thức sau : \(​​\dfrac{sin x}{1:cos x}​\)+\(\dfrac{1+cosx}{sinx}\)=\(\dfrac{2}{sinx}\)

Answer 1

đề sai;sửa \(\dfrac{sinx}{1+cosx}+\dfrac{1+cosx}{sinx}=\dfrac{2}{sinx}\)\(\left(1+cosx\ne0;sinx\ne0\right)\)

\(VT=\dfrac{sin^2x+\left(cosx+1\right)^2}{sinx\left(1+cosx\right)}=\dfrac{2+2cosx}{sinx\left(1+cosx\right)}=\dfrac{2\left(1+cosx\right)}{sinx\left(1+cosx\right)}=\dfrac{2}{sinx}\left(đpcm\right)\)

Answer 2

Đề sai nhé !

\(VT=\dfrac{sin^2x+\left(cos+1\right)^2}{sin\times\left(1+cosx\right)}=\dfrac{2\left(1+cosx\right)}{sinx\left(1+cosx\right)}=\dfrac{2}{sinx}\left(ĐPCM\right)\)