If tan B = cot(4B - 45°), what is B?

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Accepted Answer

1. Use identity: $\cot x=	an(90^\circ-x)$. So $\cot(4B-45^\circ)=	an(135^\circ-4B)$.  
2. Then $	an B=	an(135^\circ-4B)$, so $B=135^\circ-4B+k\cdot180^\circ$ for some integer $k$.  
3. Solve: $5B=135^\circ+180^\circ k$. For $k=0$, $B=27^\circ$.  
4. This matches option **(d)** and is an acute valid solution.  
FINAL_ANSWER: d

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