\(A=2cos120^0.cos10^0+sin\left(90^0+10^0\right)\)
\(=2.\left(-\dfrac{1}{2}\right).cos10^0+cos10^0\)
\(=-cos10^0+cos10^0=0\)
\(B=\dfrac{sin9}{cos9}+\dfrac{sin81}{cos81}-\dfrac{sin27}{cos27}-\dfrac{sin63}{cos63}\)
\(=\dfrac{sin9.cos81+sin81.cos9}{cos9.cos81}-\dfrac{sin27.cos63+sin63.cos27}{cos27.cos63}\)
\(=\dfrac{sin90}{\dfrac{1}{2}cos90+\dfrac{1}{2}cos72}-\dfrac{sin90}{\dfrac{1}{2}cos90+\dfrac{1}{2}cos36}\)
\(=\dfrac{2}{cos72}-\dfrac{2}{cos36}=\dfrac{2\left(cos36-cos72\right)}{cos36.cos72}=\dfrac{4sin54.sin18}{cos36.cos72}\)
\(=\dfrac{4sin\left(90-36\right).sin\left(90-72\right)}{cos36.cos72}=\dfrac{4cos36.cos72}{cos36.cos72}=4\)
