Question

Tổng các nghiệm thuộc \(\left(0;2\pi\right)\) của phương trình \(sinxcos3x-sinx+2cos3x-2=0\) là:

A. \(\dfrac{2\pi}{3}\)

B. \(2\pi\)

C. \(4\pi\)

D. 0

Answer 1

A

Answer 2

A

Answer 3

\(sinx.cos3x-sinx+2cos3x-2=0\)

\(\Leftrightarrow sinx\left(cos3x-1\right)+2\left(cos3x-1\right)=0\)

\(\Leftrightarrow\left(sinx+2\right)\left(cos3x-1\right)=0\)

\(\Leftrightarrow cos3x=1\)

\(\Leftrightarrow3x=k2\pi\)

\(\Rightarrow x=\dfrac{k2\pi}{3}\)

Do \(x\in\left(0;2\pi\right)\Rightarrow x=\left\{\dfrac{2\pi}{3};\dfrac{4\pi}{3}\right\}\)

\(\Rightarrow\dfrac{2\pi}{3}+\dfrac{4\pi}{3}=2\pi\)