We are given
Angles α and β are angles in standard position
and
α terminates in Quadrant II
β terminates in Quadrant I
and we have
[tex]sin(\alpha)=\frac{3}{5}[/tex]
we can use triangle and find cos(α)
we get
[tex]cos(\alpha)=-\frac{4}{5}[/tex]
and we have
[tex]cos(\beta)=\frac{4}{5}[/tex]
we can draw triangle
[tex]sin(\beta)=\frac{3}{5}[/tex]
now, we can use formula
[tex]cos(\alpha+\beta)=cos(\alpha)cos(\beta)-sin(\alpha)sin(\beta)[/tex]
now, we can plug values
[tex]cos(\alpha+\beta)=-\frac{4}{5}\times \frac{4}{5}-\frac{3}{5}\times \frac{3}{5}[/tex]
now, we can simplify it
[tex]cos(\alpha+\beta)=-\frac{16}{25}-\frac{9}{25}[/tex]
[tex]cos(\alpha+\beta)=-\frac{(16+9)}{25}[/tex]
[tex]cos(\alpha+\beta)=-\frac{(16+9)}{25}[/tex]
[tex]cos(\alpha+\beta)=-\frac{25}{25}[/tex]
[tex]cos(\alpha+\beta)=-1[/tex]...............Answer
