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I assume the question is about cos x = -1.

While it is true that cos x is negative in both the second and third quadrants, it reaches the value of -1 where the two quadrants meet, not inside the quadrants. The point where they meet is on the [negative] horizontal axis and x is -pi radians.

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Q: Why cos x -1 has only one solution you mean cos x is -ve both in second and third quadrants but you are just going for second quadrant taking pie n proceeding?
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