Answer:
[tex]sin(a+b)=\frac{4\sqrt{21}+2\sqrt{65}}{45}[/tex]
Step-by-step explanation:
we are given
[tex]sin(a)=\frac{4}{9}[/tex]
[tex]sin(b)=\frac{2}{5}[/tex]
Firstly, we will draw triangle
we get
[tex]cos(a)=\frac{\sqrt{65} }{9}[/tex]
[tex]cos(b)=\frac{\sqrt{21} }{5}[/tex]
now, we can sue formula
[tex]sin(a+b)=sin(a)cos(b)+cos(a)sin(b)[/tex]
now, we can plug values
[tex]sin(a+b)=\frac{4}{9}\times \frac{\sqrt{21} }{5}+\frac{\sqrt{65} }{9}\times \frac{2}{5}[/tex]
now, we can simplify it
[tex]sin(a+b)=\frac{4\sqrt{21}+2\sqrt{65}}{45}[/tex]
