Toán Lớp 11: 6sin^2x+sin2 x-1=0 Giúp mình câu này với mn ơi

Question

Toán Lớp 11:  6sin^2x+sin2 x-1=0 Giúp mình câu này với mn ơi

buianhtuan · Answer

$6sin^2x+sin2x+1=0$ $&hArr;6 frac{1-cos2x}{2}+sin2x+1=0$ $&hArr;3(1-cos2x)+sin2x+1=0$ $&hArr;-3cos2x+sin2x+4=0$ (1) $Chia 2 vế cho  sqrt{a^2+b^2}=$ $ sqrt{10}$   (1)&hArr;$ frac{-3 }{ sqrt{10}}cos2x+ frac{1 }{ sqrt{10}}sin2x=0$   Đặt $ frac{-3}{ sqrt{10}}= sin alpha$, $ frac{1}{ sqrt{10}}= cos alpha$   &rArr;$sin alpha.cos2x+sin2x.cos alpha=-4$   &hArr;$sin(2x+ alpha)=-4$ (VN)

tuminh25 · Answer

$6sin^22x+sin2x-1=0$   $&hArr;$ ( left[  begin{array}{l}sin2x= dfrac{1}{3}  sin2x=- dfrac{1}{2} end{array}  right. )    $&hArr;$ ( left[  begin{array}{l}x= dfrac{1}{2}.acrsin bigg( dfrac{1}{3} bigg)+k&pi;  x=- dfrac{1}{2}.acrsin bigg( dfrac{1}{3} bigg)+ dfrac{&pi;}{2}+k&pi;  x=- dfrac{&pi;}{12}+k&pi;  x= dfrac{7&pi;}{12}+k&pi; end{array}  right. )    $(k in  mathbb{Z})$