Question

Помогите решить алгебру 10 класс
$frac{2 sin^{2} ( alpha ) - 1}{1 - 2 cos^{2} ( alpha ) } + tan^{2} ( alpha )$
$frac{ sin^{2} (x) - cos^{2} (x) + cos^{4} (x) }{ cos^{2} (x) - sin ^{2} (x) + sin^{4} (x) }$
$frac{ sin^{2} (x) cot^{2} (x) }{1 - sin^{2} (x) } + cot^{2} (x)$
$frac{ cos^{2} ( gamma ) - cot^{2} ( gamma ) + 1 }{ sin^{2} ( gamma ) + tan^{2} ( gamma ) - 1 }$
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Answer 1

$1)frac{2Sin^{2}alpha-1}{1-2Cos^{2}alpha}+tg^{2}alpha=frac{-Cos2alpha}{-Cos2alpha}+tg^{2}alpha=1+tg^{2}alpha=frac{1}{Cos^{2}alpha}\\2)frac{Sin^{2}x-Cos^{2}x+Cos^{4}x}{Cos^{2}x-Sin^{2}x+Sin^{4}x}=frac{Sin^{2}x-Cos^{2}x(1-Cos^{2}x)}{Cos^{2}x-Sin^{2}x(1-Sin^{2}x)}=frac{Sin^{2}x-Cos^{2}x*Sin^{2}x }{Cos^{2}x-Sin^{2} x*Cos^{2}x}=frac{Sin^{2}x(1-Cos^{2}x)}{Cos^{2}x(1-Sin^{2}x)}=frac{Sin^{2}x*Sin^{2}x}{Cos^{2}x*Cos^{2}x}=frac{Sin^{4}x }{Cos^{4}x }=tg^{4}x$

$3)frac{Sin^{2}xCtg^{2}x}{1-Sin^{2}x }+Ctg^{2}x=frac{Sin^{2}x*frac{Cos^{2}x }{Sin^{2}x }}{Cos^{2}x }+Ctg^{2}x=frac{Cos^{2}x }{Cos^{2}x }+Ctg^{2}x=1+Ctg^{2}x=frac{1}{Sin^{2}x}$