Find the value of expression: `sin(2tan^(-1)(1/3))+cos(tan^(-1)2sqrt(2))`

Answer

N/a

Explanation

We have, `sin(2tan^(-1)'1/3) + cos(tan^(-1)2sqrt(2))`
`= sin[sin^(-1)[{(2xx1/3)/(1+(1/3)^(2))}] + cos (cos^(-1)'1/3) , [,' tan^(-1)x=cos^(-1)'1/(sqrt(1+x^(2))]`
`[:' 2tan^(-1)x = sin^(-1)'(2x)/(1+x^(2)),-1 le x le 1` and `tan^(-1)(2sqrt(2))=cos^(-1)'(1)/(3)`]
`=sin[sin^(-1)((2/3)/(1+((1)/(3))^(2)))]+1/3` , {`:.cos(cos^(-1)x)=x,x in[-1,1]}`
`= sin[sin^(-1)((2xx9)/(3xx10))]+1/3 = sin[sin^(-1)(3/5)]+1/3,[:' sin (sin^(-1)x)=x]`
`= 3/5+1/3=(9+5)/(15)=14/15`