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If sinA sinB sinC+cosAcosB=1, then the v...

If `sinA sinB sinC+cosAcosB=1,` then the value of sinC is

A

1

B

`1//2`

C

0

D

`-1`

Text Solution

Verified by Experts

The correct Answer is:
A
`As cos C le1`
`therefore sinA sinB sinC+cosAcosB lesin A sinB+cosA cosB`
`impliessin A sinBsinC+cosAcosBlecos(A-B)`
`implies1lecos(A-B)`
`impliescos(A-B) =1impliesA=B`
`thereforesinA sinBsinC+cosAcosB=1`
`impliessin^(2)A sinC+cos^(2)A=1`
This is satisfied by `sin C =1` only.
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