Question

Me ayudáis en esta porfavor

Answer 1

Sea x=sen(a+b)cos(a-b)

sabemos que:

sen(a+b)=sen(a)cos(b)+sen(b)cos(a)

cos(a-b)=cos(a)cos(b)+sen(a)sen(b)

x=(sen(a)cos(b)+sen(b)cos(a))(cos(a)cos(b)+sen(a)sen(b))

x=sen(a)cos(a)cos^2(b)+sen(b)cos(b)sen^2(a)+sen(b)cos(b)cos^2(a)+sen(a)cos(a)sen^2(b)

factorizando

x=sen(a)cos(a)(cos^2(b)+sen^2(b))+sen(b)cos(b)(sen^2(a)+cos^2(a))...(1)

Recordemos

cos^2(b)+sen^2(b)=1

sen^2(a)+cos^2(a)=1

reemplazando esrtos valores en 1

x=sen(a)cos(a)(1)+sen(b)cos(b)(1)

x=sen(a)cos(a)+sen(b)cos(b)