Question

sin x + sin 3x + cos x = 0​

Answer 1

$sin(x)+sin(3x)+cos(x)=0\2sin(2x)cos(x)+cos(x)=0\cos(x)(2sin(2x)+1)=0\begin{cases}cos(x)=0\sin(2x)=-dfrac{1}{2}end{cases}Rightarrowbegin{cases}x=dfrac{pi}{2}+pi k\2x=-dfrac{pi}{6}+2pi k\2x=-frac{7pi}{6}+2pi kend{cases}, k in mathbb ZRightarrowbegin{cases}x=dfrac{pi}{2}+pi k\x=-dfrac{pi}{12}+pi k\x=-frac{7pi}{12}+pi kend{cases}kinmathbb Z$