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  • Value of x for which it is satisfying <img alt="(\cos ^{-1} x)^2-3\cos^{-1} x+2 >0" src="https://learn.careers360.com/latex-image/?%28%5Ccos%20%5E%7B-1%7D%20x%29%5E2-3%5Ccos%5E%7B-1%7D%20x&

Value of x for which it is satisfying (\cos ^{-1} x)^2-3\cos^{-1} x+2 >0

Option: 1

[-\infty, \cos2)U(\cos 1,\infty]


Option: 2

[-1, \cos1)U(\cos 2,1]


Option: 3

[-1, \cos2)U(\cos 1,1]


Option: 4

None of these


Answers (1)

best_answer

 

 

Domain and range of Inverse Trigonometric Function (Part 1) -

Domain and range of Inverse Trigonometric Function (Part 1)

y = cos-1(x)

                                                    \mathrm{Domain\;is\;[-1,1]\;\;and\;\;Range\;\;is\;\;\left [ 0,\pi\right ]}
 

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(\cos ^{-1} x)^2-3\cos^{-1} x+2 >0\\ (\cos^{-1}x-1)(\cos^{-1}x -2)>0\\ \cos^{-1} x<1 \ or\ cos^{-1}x>2\\ \because \cos ^{-1} x \text{ is decreasing }\\ x> \cos1 \ or\ x<\cos2 \\ x\epsilon [-1, \cos2)U(\cos 1,1]

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