Giải câu 4 bài Ôn tập chương 6 sgk Đại số 10 trang 155

Giải câu 4 bài Ôn tập chương 6 sgk Đại số 10 trang 155.

a) $\frac{2 \sin 2 α - \sin 4 α}{2 \sin 2 α + \sin 4 α}$

$= \frac{2 \sin 2 α - 2 \sin 2 α . c o s 2 α}{2 \sin 2 α + 2 \sin 2 α . c o s 2 α}$

$= \frac{1 - \cos 2 α}{1 + \cos 2 α}$

$= \frac{2 \sin^{2} α}{2 \cos^{2} α} = \tan^{2} α$

b) $\tan α (\frac{1 + \cos^{2} α}{\sin α} - \sin α)$

$= \frac{\sin α}{\cos α} (\frac{1 + \cos^{2} α - \sin^{2} α}{\sin α})$

$= \frac{\sin α}{\cos α} . \frac{2 \cos^{2} α}{\sin α}$

$= 2 \cos α$

c) $\frac{\sin (\frac{π}{4} - α) + \cos (\frac{π}{4} - α)}{\sin (\frac{π}{4} - α) - \cos (\frac{π}{4} - α)}$

$= \frac{\tan (\frac{π}{4} - α) + 1}{\tan (\frac{π}{4} - α) - 1}$

$= (\frac{\tan \frac{π}{4} - \tan α}{1 + \tan \frac{π}{4} . \tan α} + 1) : (\frac{\tan \frac{π}{4} - \tan α}{1 + \tan \frac{π}{4} . \tan α} - 1)$

$= (\frac{1 - \tan α + 1 + \tan α}{1 + \tan α}) : (\frac{1 - \tan α - 1 - \tan α}{1 + \tan α})$

$= \frac{- 1}{\tan α} = - \cot α$

d) $\frac{\sin 5 α - \sin 3 α}{2 \cos 4 α}$

$= \frac{2 \cos \frac{5 α + 3 α}{2} \sin \frac{5 α - 3 α}{2}}{2 \cos 4 α}$

$= \sin α$