Question

demostrar la siguiente igualdad.

senb x cos(a-b) + cosb x sen(a-b) = sena

Answer 1

Hola,

Demostrar la siguiente Identidad Trigonométrica:

$\sin(b) \times \cos(a - b) + \cos(b) \times \sin(a - b) = \sin(a) \\ \sin(b) ( \cos(a) \times \cos(b) + \sin(a) \times \sin(b) ) + \cos(b) ( \sin(a) \times \cos(b) - \cos(a) \times \sin(b) ) = \sin(a) \\ \cos(a) \times \cos(b) \times \sin(b) + \sin(a) \times \sin {}^{2} (b) + \sin(a) \times \cos {}^{2} (b) - \cos(a) \times \cos(b) \times \sin(b) = \sin(a) \\ \sin(a) \times \sin {}^{2} (b) + \sin(a) \times \cos {}^{2} (b) = \sin(a) \\ \sin(a) ( \sin {}^{2} (b) + \cos {}^{2} (b)) = \sin(a) \\ \sin(a) (1) = \sin(a) \\ \sin(a) = \sin(a)$
Espero que te sirva, Saludos.