Toán giải phương trình : 2cot2x-cotx=tan(x/2) 17/08/2021 By Eliza giải phương trình : 2cot2x-cotx=tan(x/2)
Giải thích các bước giải: $2\cot 2x-\cot x=\tan \dfrac{x}{2}$ $\to \cot 2x-\cot x=\tan \dfrac{x}{2}-\cot 2x$ $\to \dfrac{\cos 2x}{\sin 2x}-\dfrac{\cos x}{\sin x}=\dfrac{\sin\dfrac{x}{2}}{\cos\dfrac{x}{2}}-\dfrac{\cos 2x}{\sin 2x}$ $\to \dfrac{\cos 2x.\sin x-\sin 2x.\cos x}{\sin 2x.\sin x}=\dfrac{\sin\dfrac{x}{2}.\sin 2x-\cos\dfrac{x}{2}.\cos 2x}{\cos\dfrac{x}{2}.\sin 2x}$ $\to \dfrac{-\sin x}{\sin 2x.\sin x}=-\dfrac{\cos\dfrac{5x}{2}}{\cos\dfrac{x}{2}.\sin 2x}$ $\to\dfrac{\cos\dfrac{5x}{2}}{\cos\dfrac{x}{2}}=1$ $\to \cos\dfrac{5x}{2}=\cos\dfrac{x}{2}$ $\to x=\dfrac{4\pi n}{3},\:x=\dfrac{2\pi }{3}+\dfrac{4\pi n}{3},\:x=2\pi n,\:x=\pi +2\pi n$ Trả lời
Giải thích các bước giải:
$2\cot 2x-\cot x=\tan \dfrac{x}{2}$
$\to \cot 2x-\cot x=\tan \dfrac{x}{2}-\cot 2x$
$\to \dfrac{\cos 2x}{\sin 2x}-\dfrac{\cos x}{\sin x}=\dfrac{\sin\dfrac{x}{2}}{\cos\dfrac{x}{2}}-\dfrac{\cos 2x}{\sin 2x}$
$\to \dfrac{\cos 2x.\sin x-\sin 2x.\cos x}{\sin 2x.\sin x}=\dfrac{\sin\dfrac{x}{2}.\sin 2x-\cos\dfrac{x}{2}.\cos 2x}{\cos\dfrac{x}{2}.\sin 2x}$
$\to \dfrac{-\sin x}{\sin 2x.\sin x}=-\dfrac{\cos\dfrac{5x}{2}}{\cos\dfrac{x}{2}.\sin 2x}$
$\to\dfrac{\cos\dfrac{5x}{2}}{\cos\dfrac{x}{2}}=1$
$\to \cos\dfrac{5x}{2}=\cos\dfrac{x}{2}$
$\to x=\dfrac{4\pi n}{3},\:x=\dfrac{2\pi }{3}+\dfrac{4\pi n}{3},\:x=2\pi n,\:x=\pi +2\pi n$