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In a triangle ABC, if a, b, c are in A.P...

In a triangle ABC, if a, b, c are in A.P. and `(b)/(c) sin 2C + (c)/(b) sin 2B + (b)/(a) sin 2A + (a)/(b) sin 2B = 2`, then find the value of sin B

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The correct Answer is:
`(1)/(2)`
`(b)/(c) sin 2C + (c)/(b) sin 2B + (b)/(a) sin 2A + (a)/(b) sin 2B = 2`
`rArr 2 sin B cos C + 2 sin C cos B + 2 sin B cos A + 2 sin B cos B = 2`
`rArr sin (B + C) + sin (A + B) = 1`
`rArr sin A + sin C = 1`
`rArr sin B = (1)/(2) " " ("As " 2 sin B = sin A + sin C)`
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