Question

Доказать тождество:
1) sin2x-tgx=cos2x*tgx
2)tgx+2ctg2x=ctgx

ПОЖАЛУЙСТА, ОЧЕНЬ СРОЧНО!!!!​

Answer 1

Доказать тождество:

$sin (2x)-tg (x) = cos (2x)cdot tg (x))\sin (2x)-tg (x) = left(2cos ^2(x)-1right)tg (x)\sin (2x)-tg (x) = 2cos^2(x)tg(x)-tg (x)\sin (2x)-tg (x) = 2cos ^2(x)frac{sin (x)}{cos (x)}-tg (x)\sin (2x)-tg (x) = 2cos (x)sin (x)-tg (x)\sin (2x)-tg (x) = sin left(2xright)-tg (x)$

тождество доказано

$tg (x)+2ctg (2x)=ctg (x)\\frac{sin(x)}{cos(x)}+2cdot frac{cos(2x)}{sin(2x)}=ctg(x)\\frac{sin(2x)sin(x)+2cos(2x)cos(x)}{cos(x)sin(2x)}=ctg(x)\\frac{2cos(2x)cos(x)+2cos(x)sin(x)sin(x)}{2cos(x)cos(x)sin(x)}=ctg(x)\\frac{cos(2x)+sin^2(x)}{cos(x)sin(x)}=ctg(x)\\frac{cos^2(x)-sin^2(x)+sin^2(x)}{cos(x)sin(x)}=ctg(x)\\frac{cos^2(x)}{cos(x)sin(x)}=ctg(x)\\frac{cos(x)}{sin(x)}=ctg(x)\\ctg(x) = ctg(x)$

тождество доказано