Question

tg в квадрате альфа - sin в квадрате альфа =sin в квадрате альфа умножить на tg в квадрате альфа

Answer 1

$tg^2alpha-sin^2alpha=sin^2alphacdot tg^2alpha |cdot dfrac{1}{sin^2alpha} \dfrac{tg^2alpha}{sin^2alpha}-1=tg^2alpha Leftrightarrow left { {big{dfrac{sin^2alpha}{cos^2alphacdot sin^2alpha}-1=dfrac{sin^2alpha}{cos^2alpha} }} atop {big{alphaneq dfrac{pi}{2}+pi n, nin Z}}} right. Leftrightarrow left { {{big{dfrac{1}{cos^2alpha}-dfrac{sin^2alpha}{cos^2alpha}=1}} atop {big{alphaneq dfrac{pi}{2}+pi n, nin Z }}} right. Leftrightarrow$

$Leftrightarrowleft { {{big{dfrac{1-sin^2alpha}{cos^2alpha}=1 }} atop {big{alphaneq dfrac{pi}{2}+pi n, nin Z}}} right. Leftrightarrow left { {{big{dfrac{cos^2alpha}{cos^2alpha}=1 }} atop {big{alphaneq dfrac{pi}{2}+pi n, nin Z}}} right. Leftrightarrowleft { {{big{alphain R}} atop {big{alphaneq dfrac{pi}{2}+pi n, nin Z}}} right. Leftrightarrow \Leftrightarrow alphaneq dfrac{pi}{2}+pi n, nin Z\\\OTBET: alphaneq dfrac{pi}{2}+pi n, nin Z$