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

Explanation

We know that



`sin (2 \tan ^{-1} \frac{1}{3})+\cos (\tan ^{-1} 2 \sqrt{2})`




`sin (2 \tan ^{-1} \frac{1}{3})=\sin (\sin ^{-1} \frac{2 \times \frac{1}{3}}{1+(\frac{1}{3})^{2}})(\2 \tan ^{-1} x=\sin ^{-1} \frac{2 x}{1+x^{2}})`




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