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Question

cos1{12x2+1x21x24}=cos1x2cos1x hold for

A
x[1,1]
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B
xR
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C
x[0,1]
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D
x[1,0]
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Solution

The correct option is C x[0,1]
Given , cos1{12x2+1x21x24}=cos1x2cos1x
Since, 12x2+1x21x24 is positive and defined for all x[1,1]

Now, cos1x2 is defined for 1x21
2x2
Also,
cos1x is defined for 1x1
Also, LHS0
cos1x2cos1x0cos1x2cos1x
x[0,1]
So, LHS is defined for x[0,1]

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