1.

Let A, B, C be real numbers such that (i) (sin A, cos B) lies on a unit circle centred at origin. (ii) tan C and cot C are defined. If the minimum value of (tan C – sin A)^(2) + (cot C – cos B)^(2) is a+bsqrt(2) where a, b in I, find the valueof a^(3) + b^(3).

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