Question

tgatga+ctga=sin²a Доказать тождество

Answer 1

$frac{tgx}{tgx + ctgx} = sin^2x \ frac{tgx}{ frac{1}{ctgx} + ctgx} = sin^2x \ frac{tgx}{ frac{1 + ctg^2x}{ctgx} } = sin^2x \ frac{tgx}{ frac{1 + ctg^2x}{ctgx} } = sin^2x \ frac{tgx}{1 + ctg^2x} : ctgx = sin^2x \ frac{tgx}{1 + ctg^2x} * frac{1}{ctgx} = sinx^2 \ frac{1}{1 + ctg^2x} = sin^2x \ frac{1}{ frac{1}{sin^2x} } = sin^2x \ sin^2x = sin^2x$