Question

Докажите тождество
1-4sin^2 x=4sin(p/6-x)sin(p/6+x)

Answer 1

$1-4sin^{2}x=4sin( \frac{\pi}{6} -x)sin(\frac{\pi}{6}+x),$
$1-4sin^{2}x = 4*\frac{1}{2}(cos(\frac{\pi}{6}-x-\frac{\pi}{6}-x)-cos(\frac{\pi}{6}-x+\frac{\pi}{6}+x)),$
$1-4sin^{2}x=2cos2x-2cos\frac{\pi}{3},$
$1-4sin^{2}x=2-4sin^{2}x-2*\frac{1}{2},$
$1-4sin^{2}x-2+4sin^{2}x=-1,$
$-1=-1.$
ч. т. д.