If a<132, then the number of solutions of sin−1⁡x3+cos−1⁡x3=aπ3, is

We find thatsin−1⁡x3+cos−1⁡x3=sin−1⁡x+cos−1⁡x3−3sin−1⁡xcos−1⁡xsin−1⁡x+cos−1⁡x=π38−3sin−1⁡xcos−1⁡xπ2=π38−3π2π2−sin−1⁡xsin−1⁡x=π38−3π24sin−1⁡x+3π2sin−1⁡x2=π38+3π2sin−1⁡x2−π2sin−1⁡x=π38+3π2sin−1⁡x−π42−3π332=π332+3π2sin−1⁡x−π42⇒ sin−1⁡x3+cos−1⁡x3≥π332⇒ aπ3≥π332⇒a≥132But, it is given that a<132.Hence, for a<132, the equation has no solution.