Đáp án:
Xét VT ta có:
$\tan x + \dfrac{\cos x}{1+\sin x} = \dfrac{\sin x}{\cos x}+\dfrac{\cos x}{1+\sin x}=\dfrac{1+\sin x}{\cos x(1+\sin x)}=\dfrac{1}{\cos x}$
$\cot x + \dfrac{\sin x}{1 + \cos x} = \dfrac{\cos x}{\sin x}+ \dfrac{\sin x}{1 + \cos x}=\dfrac{1+\cos x}{\sin x(1+\cos x)}=\dfrac{1}{\sin x}$
$→ \dfrac{1}{\cos x}.\dfrac{1}{\sin x}=\dfrac{1}{\sin x.\cos x}=VP$
$→ (\tan x + \dfrac{\cos x}{1+\sin x}).(\cot x + \dfrac{\sin x}{1 + \cos x})=\dfrac{1}{\sin x.\cos x}$ (đpcm)
BẠN XEM THAM KHẢO NHA!!!
