Toán Lớp 11: sin4x=√3/2 cot(x+pi/6)=√3 sin(x-2021)=3 tan2x=1/2

Question

Toán Lớp 11:  sin4x=√3/2 cot(x+pi/6)=√3 sin(x-2021)=3 tan2x=1/2

tuanh · Answer

Giải đáp:   $a) left[ begin{array}{l} x= dfrac{ pi}{12}+ dfrac{k  pi}{2}(k  in  mathbb{Z})    x= dfrac{ pi}{6}+ dfrac{k  pi}{2}(k  in  mathbb{Z}) end{array}  right.   b) x=k   pi(k  in  mathbb{Z})   c)x  in  varnothing   d)x= dfrac{1}{2} arctan left( dfrac{1}{2} right)+ dfrac{k   pi}{2}(k  in  mathbb{Z}).$   Lời giải và giải thích chi tiết:   $a) sin 4x= dfrac{ sqrt{3}}{2}    Leftrightarrow  sin 4x= sin  left( dfrac{ pi}{3} right)    Leftrightarrow   left[ begin{array}{l} 4x= dfrac{ pi}{3}+k 2  pi(k  in  mathbb{Z})    4x= dfrac{2 pi}{3}+k 2  pi(k  in  mathbb{Z}) end{array}  right.    Leftrightarrow   left[ begin{array}{l} x= dfrac{ pi}{12}+ dfrac{k  pi}{2}(k  in  mathbb{Z})    x= dfrac{ pi}{6}+ dfrac{k  pi}{2}(k  in  mathbb{Z}) end{array}  right.   b) cot  left(x+ dfrac{ pi}{6} right)= sqrt{3}    Leftrightarrow  cot  left(x+ dfrac{ pi}{6} right)= cot  left( dfrac{ pi}{6} right)    Leftrightarrow x+ dfrac{ pi}{6}= dfrac{ pi}{6}+k   pi(k  in  mathbb{Z})    Leftrightarrow x=k   pi(k  in  mathbb{Z})   c) sin(x-2021)=3$    Phương tr&igrave;nh v&ocirc; nghiệm do $ sin(x-2021)  in [-1;1]$    $d) tan 2x= dfrac{1}{2}    Leftrightarrow  tan 2x= tan  left( arctan left( dfrac{1}{2} right) right)    Leftrightarrow 2x= arctan left( dfrac{1}{2} right)+k   pi(k  in  mathbb{Z})    Leftrightarrow x= dfrac{1}{2} arctan left( dfrac{1}{2} right)+ dfrac{k   pi}{2}(k  in  mathbb{Z}).$