cho tan $\alpha$ = $\frac{3}{2}$ .Tính Q = 3$Sin^{2}$ $\alpha$ +5$cos^{2}$$\alpha$ + cot$\alpha$ 20/08/2021 Bởi aihong cho tan $\alpha$ = $\frac{3}{2}$ .Tính Q = 3$Sin^{2}$ $\alpha$ +5$cos^{2}$$\alpha$ + cot$\alpha$
$\dfrac{1}{\cos^2\alpha}=1+\tan^2\alpha$ $\to \cos^2\alpha=\dfrac{4}{13}$ $\cot\alpha=\dfrac{1}{\tan\alpha}=\dfrac{2}{3}$ $\to Q=3\sin^2\alpha+5\cos^2\alpha+\cot\alpha=3(\sin^2\alpha+\cos^2\alpha)+2\cos^2\alpha+\cot\alpha$ $=3.1+2.\dfrac{4}{13}+\dfrac{2}{3}$ $=\dfrac{167}{39}$ Bình luận
$\dfrac{1}{\cos^2\alpha}=1+\tan^2\alpha$ $\to \cos^2\alpha=\dfrac{4}{13}$
$\cot\alpha=\dfrac{1}{\tan\alpha}=\dfrac{2}{3}$
$\to Q=3\sin^2\alpha+5\cos^2\alpha+\cot\alpha=3(\sin^2\alpha+\cos^2\alpha)+2\cos^2\alpha+\cot\alpha$
$=3.1+2.\dfrac{4}{13}+\dfrac{2}{3}$
$=\dfrac{167}{39}$