Question

СРОЧНО тотожность (1-cos^2альфа)(1+tg^2альфа)=tg^2альфа

Answer 1

$(1-Cos^{2} \alpha)(1+tg^{2}\alpha)=tg^{2}\alpha\\\\\Big(1-Cos^{2} \alpha\Big)\Big(1+tg^{2}\alpha\Big)=Sin^{2}\alpha\cdot \Big(1+\dfrac{Sin^{2}\alpha}{Cos^{2}\alpha} \Big)=\\\\=Sin^{2} \alpha\cdot\dfrac{Sin^{2}\alpha+Cos^{2}\alpha}{Cos^{2}\alpha} =Sin^{2} \alpha\cdot\dfrac{1}{Cos^{2}\alpha} =\dfrac{Sin^{2}\alpha }{Cos^{2}\alpha}=tg^{2}\alpha$

Тождество доказано