\(A=\dfrac{2\cdot cos2a\cdot cosa+2\cdot cos2a}{2\cdot sin2a\cdot cosa+2sin2a}\)
\(=\dfrac{2cos2a\left(cosa+1\right)}{2sin2a\left(cosa+1\right)}=\dfrac{cos2a}{sin2a}=cot2a\)
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