Toán Lớp 11: cot bình x/2=1/3 giúp voowisanh em

Question

Toán Lớp 11:  cot bình x/2=1/3 giúp voowisanh em

hothaibinh · Answer

Giải đáp:   $ left[ begin{array}{l} x = dfrac{2 pi}{3}+k2  pi(k  in  mathbb{Z})   x=- dfrac{2 pi}{3}+k 2 pi(k  in  mathbb{Z})  end{array}  right.$   Lời giải và giải thích chi tiết:   $ cot ^2 left( dfrac{x}{2} right)= dfrac{1}{3}         D= mathbb{R}  setminus  left {k 2  pi; k  in  mathbb{Z} right }    Leftrightarrow  left[ begin{array}{l}  cot  left( dfrac{x}{2} right) = dfrac{ sqrt{3}}{3}    cot  left( dfrac{x}{2} right) =- dfrac{ sqrt{3}}{3}  end{array}  right.    Leftrightarrow  left[ begin{array}{l}  cot  left( dfrac{x}{2} right) = cot left( dfrac{ pi}{3} right)    cot  left( dfrac{x}{2} right) = cot left(- dfrac{ pi}{3} right)  end{array}  right.    Leftrightarrow  left[ begin{array}{l} dfrac{x}{2} = dfrac{ pi}{3}+k  pi(k  in  mathbb{Z})    dfrac{x}{2} =- dfrac{ pi}{3}+k  pi(k  in  mathbb{Z})  end{array}  right.    Leftrightarrow  left[ begin{array}{l} x = dfrac{2 pi}{3}+k2  pi(k  in  mathbb{Z})   x=- dfrac{2 pi}{3}+k 2 pi(k  in  mathbb{Z})  end{array}  right.$