Question

Упростите выражение: tg (1- sin a) (1 + sin a) ​

Answer 1

Відповідь:

$sin(\alpha )*cos(\alpha )$

Покрокове пояснення:

$tg(\alpha )(1- sin(\alpha )) (1 + sin (\alpha ))=tg(\alpha )(1-sin^2(\alpha ));\\\\sin^2(\alpha )+cos^2(\alpha )=1\\cos^2(\alpha ) = 1-sin^2(\alpha )\\\\tg(\alpha )(1-sin^2(\alpha ))=tg(\alpha )*cos^2(\alpha )=\frac{sin(\alpha )}{cos(\alpha )} *cos^2(\alpha )=sin(\alpha )*cos(\alpha )$