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If [ cot inverse x ] + [ cos inverse x] = 0 where [ ] represent the greatest integer function, then the complete set of values of x is

If [ cot inverse x ] + [ cos inverse x] = 0 where [ ]   represent the greatest integer function, then the complete set of values of x is

Grade:12

1 Answers

Aditya Gupta
2081 Points
5 years ago
since cot inverse x and cos inverse x lie in [0, pi] so their greatest integer function lies in [0,3].
now, for [ cot inverse x ] + [ cos inverse x] = 0, both [cot inverse x]=0 and [cos inverse x] = 0 need to hold.
for [cot inverse x]=0, cot inverse x lies in [0,1). this means that x lies in (cot1, infinity).
similarly [ cos inverse x] = 0 or  cos inverse x lies in [0,1). so x lies in (cos1, 1].
hence the solution of x will be the intersection of both these sets
So, x lies in (cot1, 1].

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