Question

me pueden ayudar por favor a Verifica la identidad: sen2x - sen2y = sen (x + y) * sen (x – y) ​

Answer 1

Respuesta:

$sen^2x - sen^2y = sen (x + y) . sen (x – y)$

Comprobación:

$sen(x + y) .sen (x – y) = (sen(x)cos(y) + sen(y)cos(x))(sen(x)cos(y) - sen(y)cos(x)) \\ = sen {}^{2} (x)cos {}^{2} (y) - sen {}^{2} (y)cos {}^{2} (x)\\=sen {}^{2} (x)(1-sen {}^{2} (y) ) - sen {}^{2} (y)cos {}^{2} (x)\\=sen {}^{2} (x)-sen^2(x)sen{}^{2} (y) - sen {}^{2} (y)cos {}^{2} (x)\\=sen^2(x)-sen^2(y)(sen^2(x)+cos^2(x))\\=sen^2(x)-sen^2(y)$