a: \(A=cos^242^0\cdot sin30+sin^242^0\cdot cos60\)
\(=cos^242^0\cdot\dfrac{1}{2}+sin^242^0\cdot\dfrac{1}{2}\)
\(=\dfrac{1}{2}\left(sin^242^0+cos^242^0\right)=\dfrac{1}{2}\)
b: \(B=cos^210+cos^235+cos^230+cos^260+cos^255+cos^280\)
\(=\left(cos^210^0+cos^280^0\right)+\left(cos^235^0+cos^255^0\right)+\left(cos^230^0+cos^260^0\right)\)
\(=\left(cos^210^0+sin^210^0\right)+\left(cos^235^0+sin^235^0\right)+\left(cos^230^0+sin^230^0\right)\)
=1+1+1
=3