Question

Folosind formulele de reducere la primul cadran,demonstrati identitățile :a) 2cos ori (pi supra 2 - x) ori sin (pi supra 2 - x)) ori tg(pi -x) totul supra ctg (pi supra 2 +x) ori sin (pi -x) ori cos (2 pi - x) =2 :b) ctg (3pi supra 2 - x) sin (x-pi supra 2)+tg (pi +x) cos (pi + x) cos (2 pi - x) =0: c) sin (pi supra 2 - x) +sin (pi supra 2 +x) +2 cos (pi - x) =0.

Answer 1

Salut,

$\dfrac{2cos\left(\dfrac{\pi}2-x\right)\cdot sin\left(\dfrac{\pi}2-x\right)\cdot tg\left(\pi-x\right)}{ctg\left(\dfrac{\pi}2+x\right)\cdot sin(\pi-x)\cdot cos(2\pi-x)}=\dfrac{2sin x\cdot cosx\cdot(-tgx)}{(-tgx)\cdot sinx\cdot cos(-x)}=\\\\=\dfrac{2sin x\cdot cosx\cdot(-tgx)}{(-tgx)\cdot sinx\cdot cosx}=2.$

Green eyes.