\(B=\frac{-\sin\left(\frac{\pi}{2}+144^0\right)-\cos126^0}{\sin144^0-\cos126^0}.\tan\left(\pi-144^0\right)\)
\(B=\frac{-\cos144^0-\cos126^0}{\sin144^0-\cos126^0}.\left(-\tan144^0\right)\)
\(B=\frac{\sin144^0.\cos144^0+\sin144^0.\cos126^0}{\sin144^0.\cos144^0-\cos144^0.\cos126^0}\)
\(B=\frac{\sin\left(\pi+\frac{\pi}{2}-126^0\right)[\cos\left(\pi+\frac{\pi}{2}-126^0\right)+\cos126^0]}{\cos\left(\pi+\frac{\pi}{2}-126^0\right)[\sin\left(\pi+\frac{\pi}{2}-126^0\right)-\cos126^0]}\)
\(\sin\left(\pi+\frac{\pi}{2}-126^0\right)=-\sin\left(\frac{\pi}{2}-126^0\right)=-\cos126^0\)
\(\cos\left(\pi+\frac{\pi}{2}-126^0\right)=-\cos\left(\frac{\pi}{2}-126^0\right)=-\sin126^0\)
\(\Rightarrow B=\frac{-\cos126^0\left(-\sin126^0+\cos126^0\right)}{-\sin126^0\left(-\cos126^0-\cos126^0\right)}\)
\(=\cot126^0.\frac{\sin126^0-\cos126^0}{2\cos126^0}\)
\(=\cot126^0\left(\frac{1}{2}.\tan126^0-\frac{1}{2}\right)\)
\(=\frac{1}{\tan126^0}.\frac{1}{2}.\tan126^0-\frac{1}{2}.\cot126^0=\frac{1}{2}\left(1-\cot126^0\right)\)
Thế này là gọn nhất rồi đấy :<
\(B=\frac{sin126^0-cos144^0}{sin144^0-cos126^0}.tan36^0=\frac{cos36^0+sin54^0}{cos54^0+sin36^0}.tan36^0\)
\(=\frac{cos36^0+cos36^0}{sin36^0+sin36^0}.tan36^0=cot36^0.tan36^0=1\)
