a: \(A=\dfrac{sin^254^0}{tan17\cdot tan73}+cos54\cdot sin36\)
\(=\dfrac{sin^254^0}{tan17\cdot cot17}+cos54\cdot cos54\)
\(=sin^254^0+cos^254^0=1\)
b: \(tana=\dfrac{\sqrt{3}}{4}\)
=>\(\dfrac{sina}{cosa}=\dfrac{\sqrt{3}}{4}\)
=>\(sina=\dfrac{\sqrt{3}}{4}\cdot cosa\)
\(B=\dfrac{3\cdot cosa-4\cdot sina}{4sina-cosa}\)
\(=\dfrac{3\cdot cosa-4\cdot\dfrac{\sqrt{3}}{4}\cdot cosa}{4\cdot\dfrac{\sqrt{3}}{4}\cdot cosa-cosa}\)
\(=\dfrac{3cosa-\sqrt{3}\cdot cosa}{\sqrt{3}\cdot cosa-cosa}\)
\(=\dfrac{3-\sqrt{3}}{\sqrt{3}-1}=\sqrt{3}\)
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