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Question

Chứng minh rằng $:\frac{1-sinx+cosx}{1-cosx}=cot^{2}\frac{x}{2}-cot\frac{x}{2}$

never give up · Answer 1 · 4/26/2014 7:42:14 PM

Ta có:$\frac{1-sinx+cosx}{1-cosx}=\frac{1-2sin\frac{x}{2}cos\frac{x}{2}+2cos^2\frac{x}{2}-1}{1-(1-2sin^2\frac{x}{2})}$

$=\frac{-2sin\frac{x}{2}cos\frac{x}{2}+2cos^2\frac{x}{2}}{2sin^2\frac{x}{2}}=\frac{cos^2\frac{x}{2}}{sin^2\frac{x}{2}}-\frac{sin\frac{x}{2}}{cos\frac{x}{2}}=cot^2\frac{x}{2}-cot\frac{x}{2}$

Trả lời 26-04-14 07:42 PM

never give up
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score 1 · Answer 2

Bình chọn tăng 1 Bình chọn giảm

Chán chẳng có gì làm, chứng minh ngược nhé!

$VP=\frac{cos^2\frac{x}{2}}{sin^2\frac{x}{2}}-\frac{cos\frac{x}{2}}{sin\frac{x}{2}}=\frac{cos^2\frac{x}{2}-sin\frac{x}{2}.cos\frac{x}{2}}{sin^2\frac{x}{2}}$

$=\frac{\frac{1}{2}(1+cosx-sinx)}{\frac{1}{2}(1-cosx)}=\frac{1+cosx-sinx}{1-cosx}=VT$(đpcm)