a: \(=cos^2a+\left[cos\left(\dfrac{2}{3}pi\right)\cdot cosa-sin\left(\dfrac{2}{3}pi\right)\cdot sina\right]^2+\left[cos\left(\dfrac{2}{3}pi\right)\cdot cosa+sin\left(\dfrac{2}{3}pi\right)\cdot sina\right]^2\)
\(=cos^2a+\left[-\dfrac{1}{2}cosa-\dfrac{\sqrt{3}}{2}sina\right]^2+\left[-\dfrac{1}{2}cosa+\dfrac{\sqrt{3}}{2}sina\right]^2\)
\(=cos^2a+\dfrac{1}{4}cos^2a+\dfrac{\sqrt{3}}{2}\cdot cosa\cdot sina+\dfrac{3}{4}sin^2a+\dfrac{1}{4}cos^2a-\dfrac{\sqrt{3}}{2}\cdot sina\cdot cosa+\dfrac{3}{4}\cdot sin^2a\)
=3/2(sin^2a+cos^2a)
=3/2
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