Câu hỏi của Vũ Nguyễn Linh Chi

Question

chứng minh đẳng thức

cot2 α - cos2 α = cot2α.cos2α

Hoàng Tử Hà · Accepted Answer

$1+\cot^2\alpha=\frac{1}{\sin^2\alpha}$

$\Rightarrow VT=\frac{1}{\sin^2\alpha}-1-\left(1-\sin^2\alpha\right)$

$=\frac{1}{\sin^2\alpha}-2+\sin^2\alpha$

$=\frac{1-2\sin^2\alpha+\sin^4\alpha}{\sin^2\alpha}=\frac{\left(1-\sin^2\alpha\right)}{\sin^2\alpha}=\frac{\cos^2\alpha}{\sin^2\alpha}=\cot^2\alpha$

Ủa đề bài sai hử bạn?Câu trả lời: $1+\cot^2\alpha=\frac{1}{\sin^2\alpha}$

$\Rightarrow VT=\frac{1}{\sin^2\alpha}-1-\left(1-\sin^2\alpha\right)$

$=\frac{1}{\sin^2\alpha}-2+\sin^2\alpha$

$=\frac{1-2\sin^2\alpha+\sin^4\alpha}{\sin^2\alpha}=\frac{\left(1-\sin^2\alpha\right)}{\sin^2\alpha}=\frac{\cos^2\alpha}{\sin^2\alpha}=\cot^2\alpha$

Ủa đề bài sai hử bạn?