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Consider a non-zero triangle ABC with AB...

Consider a non-zero triangle ABC with AB = c, BC = a and CA = b. If `|[1,a,b],[1,c,a],[1,b,c]|=0`, then what is the value of `sin A + cos B + tan C?`

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|[1,a, bc] ,[1, b, ca], [1, c, ab]| = (a-b)(b-c)(c-a)