If  α=sin−1⁡32+sin−1⁡13 and β=cos−1⁡32+cos−1⁡13, then

From given equations, it can be seen that α+β=πsince sin−1⁡x+cos−1⁡x=π2∀xAlso, α=π3+sin−1⁡13<π3+sin−1⁡12as sinθ is increasing in  [0,π2]∴ α<π3+π6=π2⇒β>π2>α⇒α<β