sin\(x\) = \(\frac{1}{3}\), 90o < \(x\)< 180o. Tính A = \(\frac{tanx+3cotx+1}{tanx+cotx}\)
sinα = \(\frac{2}{3}\). Tính A = \(\frac{cot\alpha-tan\alpha}{cot\alpha+tan\alpha}\)
tanα = \(\sqrt{2}\). Tính B = \(\frac{sin\alpha-cos\alpha}{sin^3\alpha+3cos^3\alpha+2sin\alpha}\)
tanα = 3. Tính C = \(\frac{sin^2\alpha-5cos^2\alpha}{2sin^2\alpha+3sin\alpha.cos\alpha+cos^2\alpha}\)
\(90^0< x< 180^0\Rightarrow cosx< 0\Rightarrow cosx=-\sqrt{1-sin^2x}=-\frac{2\sqrt{2}}{3}\)
\(\Rightarrow\left\{{}\begin{matrix}tanx=\frac{sinx}{cosx}=-\frac{\sqrt{2}}{4}\\cotx=\frac{1}{tanx}=-2\sqrt{2}\end{matrix}\right.\) \(\Rightarrow A=\) thế số bấm máy
\(A=\frac{cota-tana}{cota+tana}=\frac{\frac{cosa}{sina}-\frac{sina}{cosa}}{\frac{cosa}{sina}+\frac{sina}{cosa}}=\frac{cos^2a-sin^2a}{cos^2a+sin^2a}=cos^2a-sin^2a=1-2sin^2a=1-2\left(\frac{2}{3}\right)^2\)
\(B=\frac{\frac{sina}{cos^3a}-\frac{cosa}{cos^3a}}{\frac{sin^3a}{cos^3a}+\frac{3cos^3a}{cos^3a}+\frac{2sina}{cos^3a}}=\frac{tana\left(1+tan^2a\right)-\left(1+tan^2a\right)}{tan^3a+3+2tana\left(1+tan^2a\right)}=...\) thế số bấm máy
\(C=\frac{\frac{sin^2a}{cos^2a}-\frac{5cos^2a}{cos^2a}}{\frac{2sin^2a}{cos^2a}+\frac{3sina.cosa}{cos^2a}+\frac{cos^2a}{cos^2a}}=\frac{tan^2a-5}{2tan^2a+3tana+1}=...\) bấm máy
