Cho \({\rm{cot}}x = - 2\). Tính \(D = \dfrac{{{\rm{sin}}x - {\rm{sin}}2x}}{{{\rm{cos}}2x - {\rm{cos}}x +
Cho \({\rm{cot}}x = - 2\). Tính \(D = \dfrac{{{\rm{sin}}x - {\rm{sin}}2x}}{{{\rm{cos}}2x - {\rm{cos}}x + 1}}\)
Ta có: \(D = \dfrac{{{\rm{sin}}x - {\rm{sin}}2x}}{{{\rm{cos}}2x - {\rm{cos}}x + 1}} = \dfrac{{{\rm{sin}}x - 2{\rm{sin}}x{\rm{cos}}x}}{{2{\rm{co}}{{\rm{s}}^2}x - 1 - {\rm{cos}}x + 1}}\)
\( = \dfrac{{{\rm{sin}}x\left( {1 - 2{\rm{cos}}x} \right)}}{{{\rm{cos}}x\left( {2{\rm{cos}}x - 1} \right)}} = - \dfrac{{{\rm{sin}}x}}{{{\rm{cos}}x}} = - {\rm{tan}}x\)
Lại có: \({\rm{tan}}x \cdot {\rm{cot}}x = 1 \Leftrightarrow - {\rm{tan}}x \cdot {\rm{cot}}x = - 1\)
\( \Rightarrow D = - {\rm{tan}}x = \dfrac{{ - 1}}{{{\rm{cot}}x}} = \dfrac{1}{2}\)
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