Question

sinx+sin3x+cosx+cos3x=0

Answer 1

$2cdot sinfrac{x+3x}{2}cdot cosfrac{x-3x}{2}+2cdot cosfrac{x+3x}{2}cdot cosfrac{x-3x}{2}=0\ 2cdot sin2xcdot cosx+2cdot cos2xcdot cosx=0\ 2cdot cosx(sin2x+cos2x)=0$

cosx=0

$x_{1}=frac{pi}{2}+pi n$

sin2x=-cos2x

$frac{sin2x}{cos2x}=-1$

tg2x=-1

x$2x_{2}=-frac{pi}{2}+pi n, n eZ \ x_{2}=-frac{pi}{4}+frac{pi n}{2}, n eZ$