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The total number of solution of |cotx|=c...

The total number of solution of `|cotx|=cotx+1/(sinx),x in [0,3pi]` , is equal to 1 (b) 2 (c) 3 (d) 0

A

1

B

2

C

3

D

0

Text Solution

Verified by Experts

The correct Answer is:
B
`|cot x|=cot x+ 1/(sin x)`
If `cot x gt 0`
`rArr cot x=cot x+ 1/(sin x) =0`
`rArr 1/(sin x)=0`, which is not possible.
If `cot x le 0`
`rArr -cot x cot x +1/(sin x)`
`rArr -2 cot x = 1/(sinx)`
or `cos x=-1/2`
`rArr x=(2pi)/3, (8pi)/3`
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