Question

Giải phương trình sau:

a. tan x(1+cot² x)=2

b. cos x(tan x +2cos x) -2=0

Answer 1

a. ĐKXĐ: ...

\(1+cot^2x=\frac{2}{tanx}\)

\(\Leftrightarrow1+cot^2x=2cotx\)

\(\Leftrightarrow\left(cotx-1\right)^2=0\Leftrightarrow cotx=1\)

\(\Rightarrow x=\frac{\pi}{4}+k\pi\)

b. ĐKXĐ: ...

\(cosx\left(\frac{sinx}{cosx}+2cosx\right)-2=0\)

\(\Leftrightarrow sinx+2cos^2x-2=0\)

\(\Leftrightarrow sinx-2\left(1-cos^2x\right)=0\)

\(\Leftrightarrow sinx-2sin^2x=0\)

\(\Leftrightarrow\left[{}\begin{matrix}sinx=0\\sinx=\frac{1}{2}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=k\pi\\x=\frac{\pi}{6}+k2\pi\\x=\frac{5\pi}{6}+k2\pi\end{matrix}\right.\)