Toán Lớp 9: Cho tan x = 2 tính sinx, cosx, cotx

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1. $$\begin{gathered} Ta có:cotx=\frac{1}{\tan x}=\frac{1}{2} \\ 1+{\tan }^{2}x=\frac{1}{{\cos }^{2}x} \\ =>{\cos }^{2}x=\frac{1}{1+{\tan }^{2}x}=\frac{1}{1+2^2}=\frac{1}{5} \\ Do x<90=>\cos x>0=>\cos x=\sqrt{\frac{1}{5}}=\frac{\sqrt{5}}{5} \\ \tan x=\frac{\sin x}{\cos x}=>\sin x=\cos x.\tan x=\frac{\sqrt{5}}{5}.2=\frac{2\sqrt{5}}{5} \\ Vậy \sin x=\frac{2\sqrt{5}}{5}; \cos x=\frac{\sqrt{5}}{5}; \tan x=\frac{1}{2} \end{gathered}$$

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