Giúp mình với Tính sin , cos , cotg biết tan A = 2cm 12/08/2021 Bởi Reagan Giúp mình với Tính sin , cos , cotg biết tan A = 2cm
Ta có: $tanA = 2$ $\Rightarrow cotA = \dfrac{1}{2}$ $\Rightarrow tanA + cotA = \dfrac{5}{2}$ $\Leftrightarrow \dfrac{1}{sinAcosA} = \dfrac{5}{2}$ $\Leftrightarrow sinAcosA = \dfrac{2}{5}$ $\Leftrightarrow sinA = \dfrac{2}{5cosA}$ Ta lại có: $sin^2A + cos^2A = 1$ $\Rightarrow \dfrac{4}{25cos^2A} + cos^2A = 1$ $\Leftrightarrow 25cos^4A – 25cos^2A + 4 = 0$ $\Leftrightarrow \left[\begin{array}{l}cosA = \pm \dfrac{2}{\sqrt5}\\cosA = \pm \dfrac{1}{\sqrt5}\end{array}\right.$ $\Leftrightarrow \left[\begin{array}{l}sinA = \pm \dfrac{1}{\sqrt5}\\sinA = \pm \dfrac{2}{\sqrt5}\end{array}\right.$ Bình luận
$\tan A=2$ $\Rightarrow \cot A=\dfrac{1}{2}$ $\dfrac{1}{\cos^2A}=1+\tan^2A$ $\Leftrightarrow \cos A=\dfrac{2}{\sqrt5}$ $\sin A=\sqrt{1-\cos^2A}=\dfrac{1}{\sqrt5}$ Bình luận
Ta có: $tanA = 2$
$\Rightarrow cotA = \dfrac{1}{2}$
$\Rightarrow tanA + cotA = \dfrac{5}{2}$
$\Leftrightarrow \dfrac{1}{sinAcosA} = \dfrac{5}{2}$
$\Leftrightarrow sinAcosA = \dfrac{2}{5}$
$\Leftrightarrow sinA = \dfrac{2}{5cosA}$
Ta lại có: $sin^2A + cos^2A = 1$
$\Rightarrow \dfrac{4}{25cos^2A} + cos^2A = 1$
$\Leftrightarrow 25cos^4A – 25cos^2A + 4 = 0$
$\Leftrightarrow \left[\begin{array}{l}cosA = \pm \dfrac{2}{\sqrt5}\\cosA = \pm \dfrac{1}{\sqrt5}\end{array}\right.$
$\Leftrightarrow \left[\begin{array}{l}sinA = \pm \dfrac{1}{\sqrt5}\\sinA = \pm \dfrac{2}{\sqrt5}\end{array}\right.$
$\tan A=2$
$\Rightarrow \cot A=\dfrac{1}{2}$
$\dfrac{1}{\cos^2A}=1+\tan^2A$
$\Leftrightarrow \cos A=\dfrac{2}{\sqrt5}$
$\sin A=\sqrt{1-\cos^2A}=\dfrac{1}{\sqrt5}$