Toán Lớp 11: sin2x + cosx =( 2sinx +1)( 3cosx -1) ????

Question

Toán Lớp 11:  sin2x + cosx =( 2sinx +1)( 3cosx -1)  ????

hienchaudiem · Answer

Giải đáp:   $S= left {- dfrac{ pi}{6}+k2 pi; dfrac{7 pi}{6}+k2 pi; dfrac{ pi}{3}+k2 pi;- dfrac{ pi}{3}+k2 pi , bigg{|} ,k in mathbb Z right }$   Lời giải và giải thích chi tiết:   $ sin2x+ cos x=(2 sin x+1)(3 cos x-1)$   $&hArr;2 sin x cos x+ cos x=(2 sin x+1)(3 cos x-1)$   $&hArr; cos x(2 sin x+1)=(2 sin x+1)(3 cos x-1)$   $&hArr;(2 sin x+1)(2 cos x-1)=0$   $&hArr; left[  begin{array}{l}2 sin x+1=0  2 cos x-1=0 end{array}  right.&hArr; left[  begin{array}{l} sin x=- dfrac{1}{2}   cos x= dfrac{1}{2} end{array}  right.$   $&hArr; left[  begin{array}{l}x=- dfrac{ pi}{6}+k2 pi  x= dfrac{7 pi}{6}+k2 pi  x= dfrac{ pi}{3}+k2 pi  x=- dfrac{ pi}{3}+k2 pi end{array}  right. , ,(k in mathbb Z)$   V&acirc;̣y $S= left {- dfrac{ pi}{6}+k2 pi; dfrac{7 pi}{6}+k2 pi; dfrac{ pi}{3}+k2 pi;- dfrac{ pi}{3}+k2 pi , bigg{|} ,k in mathbb Z right }$.

thienthanh · Answer

sin2x+cosx=(2sinx+1)(3cosx-1)$ $<=>2sinxcosx+cosx=(2sinx+1)(3cosx-1)$ $<=>cosx(2sinx+1)=(2sinx+1)(3cosx-1)$ $<=>(2sinx+1)(cosx-3cosx+1)=0$ $<=>(2sinx+1)(1-2cosx)=0$ $<=> ( left[ begin{array}{l} sin(x)= dfrac{-1}{2} cos(x)= dfrac{1}{2} end{array} right. ) Tự tính nốt