Which of the following is the solution set of the equation sin−1⁡x=cos−1⁡x+sin−1⁡(3x−1)?

For the existence of the  given equation, we must have−1≤x≤1 and −1≤3x−1≤1⇒0≤x≤23Now,sin−1⁡x=cos−1⁡x+sin−1⁡(3x−1)⇒ sin−1⁡x−cos−1⁡x=sin−1⁡(3x−1)⇒ 2sin−1⁡x−π2=sin−1⁡(3x−1)⇒    sin⁡2sin−1⁡x−π2=sin⁡sin−1⁡(3x−1)⇒    −cos⁡2sin−1⁡x=3x−1⇒    −1−2sin2⁡sin−1⁡x=3x−1⇒    −1−2x2=3x−1⇒    2x2−3x=0⇒x=0,32⇒x=0                         [∵0≤x≤2/3]