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The variable `x` satisfying the equation `|sinxcosx|+sqrt(2+tan^2 x+cot^2x)=sqrt(3)` belongs to the interval `(a) [0,pi/3]` (b) `(pi/3,pi/3)` (c) `[(3pi)/4,pi]` (d) none-existent

A

`[0,pi/3]`

B

`(pi/3pi/2)`

C

`[(3pi)/4,pi)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
D
`abs(sinxcosx)+abs(tanx+cotx)=sqrt3`
`or abs(sinxcosx)+1/abs(sinxcosx)=sqrt3`
But `abs(sinxcosx)+1/(abs(sinxcosx))ge2`
hence, no solution.
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