CM hệ thức sau: a) sin(x+y).sin(x-y) = $sin^{2}$ x - $sin^{2}$ y b) tan x + tan y = $\frac{2.sin(x+y)}{cos(x+y)+cos(x-y)}$

b,

$VP=\dfrac{2\sin(x+y)}{\cos(x+y)+\cos(x-y)}$

$=\dfrac{2\sin(x+y)}{2\cos x\cos y}$

$=\dfrac{\sin(x+y)}{\cos x\cos y}$

$=\dfrac{\sin x\cos y+\sin y\cos x}{\cos x\cos y}$

$=\dfrac{\sin x}{\cos x}+\dfrac{\sin y}{\cos y}$

$=\tan x+\tan y$

$=VT$

a,

$VT=\sin(x+y)\sin(x-y)$

$=\dfrac{-1}{2}\left(\cos 2x-\cos2y\right)$

$=\dfrac{-1}{2}\left(1-2\sin^2x-1+2\sin^2y\right)$

$=\sin^2x-\sin^2y$

$=VP$