Question

Упростить тригонометрическое выражение)

Answer 1

$mathtt{[sin(pi+alpha)+cos(frac{pi}{2}+alpha)]^2+[cos(2pi-alpha)-sin(frac{3pi}{2}-alpha)]^2=}\mathtt{(-sinalpha-sinalpha)^2+(cosalpha-(-cosalpha))^2=(2sinalpha)^2+(2cosalpha)^2=4}$

$mathtt{[tg(frac{pi}{2}-alpha)-ctg(frac{pi}{2}+alpha)]^2-[ctg(pi+alpha)+ctg(frac{3pi}{2}+alpha)]^2=}\mathtt{(ctgalpha+tgalpha)^2-(ctgalpha-tgalpha)^2=2tgalpha*2ctgalpha=4tgalpha ctgalpha=4}$