Giải thích các bước giải:

Ta có:

$\cos(x-\dfrac{3\pi}4)+\cos(x+\dfrac{\pi}3)=0$

$\to \cos(x-\dfrac{3\pi}4)=-\cos(x+\dfrac{\pi}3)$

$\to \cos(x-\dfrac{3\pi}4)=\cos(\pi-(x+\dfrac{\pi}3))$

$\to \cos(x-\dfrac{3\pi}4)=\cos(\dfrac23\pi-x)$

$\to x-\dfrac34\pi=\dfrac23\pi-x+k2\pi \to x=\dfrac{17\pi}{24}+k\pi$ $ 

Hoặc $x-\dfrac34\pi=-(\dfrac23\pi-x)+k2\pi$

$\to -\dfrac34\pi=-\dfrac23\pi+k2\pi$ vô lý