Chứng minh: (1+cos x)/sin x – sin x/(1+cos x) = 2cot x 05/09/2021 Bởi Kaylee Chứng minh: (1+cos x)/sin x – sin x/(1+cos x) = 2cot x
$VT=\dfrac{1+\cos x}{\sin x}-\dfrac{\sin x}{1+\cos x}$ $=\dfrac{(1+\cos x)^2-\sin^2x}{\sin x(1+\cos x)}$ $=\dfrac{1+2\cos x+\cos^2x-\sin^2x}{\sin x(1+\cos x)}$ $=\dfrac{2\cos x+2\cos^2x}{\sin x(1+\cos x)}$ $=\dfrac{2\cos x(1+\cos x)}{\sin x(1+\cos x)}$ $=\dfrac{2\cos x}{\sin x}$ $=2\cot x$ $=VP$ Bình luận
$VT=\dfrac{1+\cos x}{\sin x}-\dfrac{\sin x}{1+\cos x}$
$=\dfrac{(1+\cos x)^2-\sin^2x}{\sin x(1+\cos x)}$
$=\dfrac{1+2\cos x+\cos^2x-\sin^2x}{\sin x(1+\cos x)}$
$=\dfrac{2\cos x+2\cos^2x}{\sin x(1+\cos x)}$
$=\dfrac{2\cos x(1+\cos x)}{\sin x(1+\cos x)}$
$=\dfrac{2\cos x}{\sin x}$
$=2\cot x$
$=VP$