Question

Основы тригонометрии
Упростить:
tg²a*cos²a+ctg²a*sin²a
а=альфа

Answer 1

$boldsymbol{tg^2alpha cdot cos^2alpha +ctg^2alpha cdot sin^2alpha =}\\=dfrac{sin^2alpha }{cos^2alpha }cdot cos^2alpha+dfrac{cos^2alpha }{sin^2alpha }cdot sin^2alpha=\\=sin^2alpha+cos^2alphaboldsymbol{=1}$

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Использованы формулы

$tg~alpha =dfrac{sinalpha }{cosalpha }~;~~~ctg~alpha =dfrac{cosalpha }{sinalpha }\\cos^2alpha+sin^2alpha=1$