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Let theta in [0,4pi] satisfy the equatio...

Let `theta in [0,4pi]` satisfy the equation `(sintheta+2)(sintheta+3)(sintheta+4)=6.` If the sum of all the values of `theta` is of the form `kpi` , then the value of `k` is 6 (b) 5 (c) 4 (d) 2

A

6

B

5

C

4

D

2

Text Solution

Verified by Experts

The correct Answer is:
B
`(sin theta+2) (sin theta+3) (sin theta+4) =6`
`L.H.S. ge 6` and `R.H.S. =6`
Therefore, equality only holds if
`sin theta=-1 or theta =3pi//2, 7 pi//2`
`:.` Sum `=5pi =lt k=5`
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