a) \(4{a^2}{\cos ^2}{60^0} + 2ab.{\cos ^2}{180^0} + \dfrac{4}{3}{b^2}{\cos ^2}{30^0}\)\( = 4{a^2}.\dfrac{1}{4} + 2ab.1 + \dfrac{4}{3}{b^2}.\dfrac{3}{4}\)\( = {a^2} + 2ab + {b^2} = {(a + b)^2}\)
b) \(\left( {a\sin {{90}^0} + b\tan {{45}^0}} \right)\)\(\left( {a\cos {0^0} + b\cos {{180}^0}} \right)\) \( = \left( {a.1 + b.1} \right)\left( {a.1 + b.( - 1)} \right)\)\( = \left( {a + b} \right)\left( {a - b} \right) = {a^2} - {b^2}\).
