If \( \sin A=\frac{1}{\sqrt{5}} \) and \( \cos B=\frac{3}{\sqrt{10}} \), where \( A, B \) are po...

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If \( \sin A=\frac{1}{\sqrt{5}} \) and \( \cos B=\frac{3}{\sqrt{10}} \), where \( A, B \) are positive acute angles, prove that \( A+B=45^{\circ} \)
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