Giải thích các bước giải:
$A=\sin7x-2\sin x(\cos4x+\cos6x)-\cos\left ( 3x-\dfrac{\pi}{2} \right )+1\\
=\sin7x-2\sin x\cos4x-2\sin x\cos6x-\left ( \cos3x\cos\dfrac{\pi}{2}+\sin3x\sin\dfrac{\pi}{2} \right )+1\\
=\sin7x-2.\dfrac{1}{2}\left (\sin (x-4x)+\sin(x+4x) \right )-2.\dfrac{1}{2}(\sin (x-6x)+\sin(x+6x))-\left ( \cos3x.0+\sin3x.1 \right )+1\\
=\sin7x-\left (-\sin3x+\sin5x \right )-(-\sin 5x+\sin7x)-\sin3x +1\\
=\sin7x+\sin3x-\sin5x +\sin 5x-\sin7x-\sin3x +1\\
=1$