Tính:
B= $\frac{2cos^{2}\alpha+sin\alpha.cos\alpha-sin^{2}\alpha}{sin^{2}\alpha+3cos^2\alpha-4}$ biết cota =2
Tính: B= $\frac{2cos^{2}\alpha+sin\alpha.cos\alpha-sin^{2}\alpha}{sin^{2}\alpha+3cos^2\alpha-4}$ biết cota =2
By Josephine
By Josephine
Tính:
B= $\frac{2cos^{2}\alpha+sin\alpha.cos\alpha-sin^{2}\alpha}{sin^{2}\alpha+3cos^2\alpha-4}$ biết cota =2
`B=(2cot^2a+cota-1)/(1+3cota-4/(sin^2a))`
`=(2cot^2a+cota-1)/(1+3cot^2a-4(1+cot^2a))`
`=(2.2^2+2-1)/(1+3.2^2-4(1+2^2)`
`=(-9)/(7)`
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Trả lời:
$\begin{array}{l}B=\dfrac{2\cos^2\alpha+\sin\alpha.\cos\alpha-\sin^2\alpha}{\sin^2\alpha+3\cos^2\alpha-4}=\dfrac{2\cos^2\alpha+\sin\alpha.\cos\alpha-\sin^2\alpha}{\sin^2\alpha+3\cos^2\alpha-4(\sin^2\alpha+\cos^2\alpha)}\\=\dfrac{2\cos^2\alpha+\sin\alpha.\cos\alpha-\sin^2\alpha}{-3\sin^2\alpha-\cos^2\alpha}=\dfrac{\dfrac{2\cos^2\alpha}{\sin^2\alpha}+\dfrac{\sin\alpha.\cos\alpha}{\sin^2\alpha}-\dfrac{\sin^2\alpha}{\sin^2\alpha}}{\dfrac{-3\sin^2\alpha}{\sin^2\alpha}-\dfrac{\cos^2\alpha}{\sin^2\alpha}}\\=\dfrac{2\cot^2\alpha+\cot\alpha-1}{-3-\cot^2\alpha}=\dfrac{2.2^2+2-1}{-3-2^2}=-\dfrac{9}{7}\end{array}$