Question

Упростить тригонометрическое выражение)

Answer 1

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

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