tính cos, tan, cot biết sin=1/5

Đáp án:

Giải thích các bước giải: \(\begin{array}{*{20}{l}}{\sin x = \frac{1}{5}}\\{*ta{\mkern 1mu} co:{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {{\sin }^2}x + \cos {{\mkern 1mu} ^2}x = 1}\\{ \Rightarrow cos{\mkern 1mu} x = \pm \sqrt {1 - {{\sin }^2}x} = \pm \sqrt {1 - {{\left( {\frac{1}{5}} \right)}^2}} = \pm \sqrt {1 - \frac{1}{{25}}} = \pm \sqrt {\frac{{24}}{{25}}} = \pm \frac{{2\sqrt 6 }}{5}}\\{ \Rightarrow cot{\mkern 1mu} x = \frac{{cosx}}{{\sin x}} = \frac{{ \pm \frac{{2\sqrt 6 }}{5}}}{{\frac{1}{5}}} = \pm 2\sqrt 6 }\\{ \Rightarrow \tan x = \frac{1}{{\cot {\mkern 1mu} x}} = \frac{1}{{ \pm 2\sqrt 6 }}{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} \left( {vi{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} \tan {\mkern 1mu} x.\cot {\mkern 1mu} x = 1} \right)}\end{array}\)