If `sinalpha=(1)/(3) and cosbeta=(4)/(5), " then find " sin(alpha+beta)`.

Explanation

Given, `sinalpha =(1)/(3)`
`cosalpha=(sqrt8)/(3)`
`cosbeta=(4)/(5)`
`sinbeta=(3)/(5)`
`sin(alpha+beta)=sinalpha cosbeta+cosalpha sinbeta` `=(1)/(3)*(4)/(5)+(sqrt8)/(3)*(3)/(5)=(4+3sqrt8)/(15)`.
`sin(alpha+beta)=(4+3sqrt3)/(15)`.