Question

Найдите cosx^8-sinx^8,если tgx=0.5

Answer 1

$tg x=0.5;ctg x=frac{1}{tg x}=frac{1}{0.5}=2$
$sin^2 x=frac{1}{1+ctg^2 x}=frac{1}{1+2^2}=frac{1}{5}$
$cos^2 x=frac{1}{1+tg^2 x}=frac{1}{1+0.5^2}=frac{4}{5}$
$(cos x)^8-(sin x)^8=(cos^2 x)^4-(sin^2 x)^4=\\(frac{4}{5})^4-(frac{1}{5})^4=frac{4^4-1}{5^4}=frac{255}{625}=frac{51}{125}$