Question

Ecuaciones trigonometricas:

-3senx+ cos^2 x=3

tanx-senx=0

Answer 1

1.) Transformamos toda la ecuación en función de seno:
${-3\sin x + \cos ^2x =3}\\\\{-3\sin x +1 -\sin^2x=3}\\\\{\sin^2x+3\sin x +2=0}\\\\{\text{resolvemos como sexto caso de factorizaci\'on:}}\\\\{(\sin x +2)(\sin x +1)=0}\\\\\\{\sin x+ 2=0}\\{\sin x= -2}\\{x=\sin ^{-1}(-2)}\\{\mathbf{soluci\'on\ inadmisible}}\\\\{\sin x +1 =0}\\{\sin x = -1}\\{x=\sin^{-1}(-1)}\\{x= \mathbf{-90^{\circ}}}\\\\{2.)\text{usaremos las identidades trigonometricas:}}\\{\tan x - \sin x=0}\\\\{\frac{\sin x}{\cos x} -\sin x=0}\\\\{\sin x - \sin x . \cos x=0}\\\\{\sin x(1- \cos x) =0}\\\\\\{\sin x= 0}\\{x= \sin^{-1}(0)}\\{x= \mathbf{0^{\circ}}}\\\\{1-\cos x=0}\\{\cos x =1}\\{x= \cos ^{-1} (1)}\\{x=\mathbf{0^{\circ}}}\\\\{\mathbf{salu2.!!\ :)}}\\{\mathbf{Wellington}}$