Giải thích các bước giải:
$a)
VT=\dfrac{\sin x+\sin 4x+\sin7x}{\cos x+\cos4x+\cos7x}\\
=\dfrac{(\sin x+\sin7x)+\sin4x}{(\cos x+\cos7x)+\cos4x}\\
=\dfrac{2\sin\dfrac{x+7x}{2}\cos\dfrac{x-7x}{2}+\sin4x}{2\cos\dfrac{x+7x}{2}\cos\dfrac{x-7x}{x}+\cos4x}\\
=\dfrac{2\sin4x\cos3x+\sin4x}{2\cos4x\cos3x+\cos4x}\\
=\dfrac{2\sin4x(\cos3x+1)}{2\cos4x(\cos3x+1)}\\
=tan4x=VP\\
b)
VT=\dfrac{\sin2x-\sin4x}{1-\cos2x+\cos4x}\\
=\dfrac{\sin2x-2\sin2x\cos2x}{}{1-\cos2x+2\cos^22x-1}\\
=\dfrac{\sin2x(1-2\cos2x)}{\cos2x(2\cos2x-1)}\\
=\dfrac{-\sin2x(2\cos2x-1)}{\cos2x(2\cos2x-1)}\\
=-tan2x$
