If $\sin a+\sin b=\sqrt{\frac{5}{3}}$ and $\cos a+\cos b=1$, then $\cos (a-b)$ is equal to

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Professor PC Thomas Classes · Answer

Square and add equations: $2 + 2\cos(a-b) = 5/3 + 1 \Rightarrow \cos(a-b) = 1/3$.