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Given that `csc(theta)= -7/5` and that `theta` lies in the 4th quadrant find `cot(theta)`

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Given that `csc(theta)= -7/5` and that `theta` lies in the 4th quadrant find `cot(theta)`

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It is given that `csc theta = -7/5` .

=> `sin theta = -5/7`

`cos theta = sqrt(1 - (-5/7)^2)`

=> `sqrt(24)/7`

`cot theta = cos theta/sin theta`

=> `sqrt 24/(-5)`

=> `-sqrt 24/5`

The required value of `cot theta` = `-2*sqrt 6/5`

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