giải phương trình: $2cos4x+cos2x=1+\sqrt{3}sin2x$
giải phương trình: $2cos4x+cos2x=1+\sqrt{3}sin2x$
Started By Mr An, 21-03-2017 - 08:45
#1
Posted 21-03-2017 - 08:45
#2
Posted 21-03-2017 - 11:21
giải phương trình: $2cos4x+cos2x=1+\sqrt{3}sin2x$
Ta có: $2cos(4x)+cos(2x)=1+\sqrt{3}sin(2x)$
$\iff 4cos^2(2x)-2+cos(2x)=1+\sqrt{3}sin(2x)\iff (cos(2x)+1)(4cos(2x)-3)=\sqrt{3}sin(2x)$.
$\iff 2cos^2(x)(8cos^2(x)-7)=2\sqrt{3}cos(x)sin(x)$
$\iff cos(x)[8cos^3(x)-7cos(x)-\sqrt{3}sin(x)]=0$.
$\iff \left\{\begin{matrix} cos(x)=0\\cos(3x)=cos(x-\frac{\pi}{3}) \end{matrix}\right.$
$\iff \left\{\begin{matrix} x=\frac{\pi}{2}+k\pi\\x=\frac{-\pi}{6}+\frac{k\pi}{2}\\ x=\frac{\pi}{12}+\frac{k\pi}{4} \end{matrix}\right.(x\in \mathbb{Z})$
Edited by tritanngo99, 21-03-2017 - 11:22.
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