Chứng minh rằng: \(\dfrac{\sin\alpha+\cos\alpha-1}{1-\cos\alpha}\)=\(\dfrac{2\cdot\cos\alpha}{\sin\alpha-\cos\alpha+1}\)

CMR: (\(\dfrac{2}{\sqrt{6}-1}+\dfrac{3}{\sqrt{6}-2}+\dfrac{3}{\sqrt{6}-3}\))\(\cdot\dfrac{5}{9\sqrt{6}+4}=\dfrac{1}{2}\)

Giải dùm vs

\(\Delta ABC\) nhọn có : \(AH\perp BC;BI\perp AC;CK\perp AB\).Chứng minh rằng: \(S_{HIK}=\left(1-\cos^2A-\cos^2B-\cos^2C\right)\cdot S_{ABC}\)

\(\Delta ABC\) có phân giác AD , AB= b , AC= c , góc A= 2\(\alpha\) (\(\alpha\)<\(45^o\)).CMR: AD=\(\dfrac{2\cdot b\cdot c\cdot\cos\alpha}{b+c}\)

\(\dfrac{1}{\sqrt{2}+\sqrt{3}}+\dfrac{1}{\sqrt{3}+\sqrt{4}}+....+\dfrac{1}{\sqrt{2005}+\sqrt{2006}}\)

Giải chi tiết dùm mình hem