\(\alpha>0\Rightarrow\cos\left(40^0+\alpha\right)>0\Rightarrow\cos\left(40^0+\alpha\right)=\sqrt{1-\left[\sin^2\left(40^0+\alpha\right)\right]}=\sqrt{1-a^2}\)
\(\cos\left(70^0+\alpha\right)=\cos\left(30^0+40^0+\alpha\right)\)
\(=\cos30^0.\cos\left(40^0+\alpha\right)+\sin30^0.\sin\left(40^0+\alpha\right)\)
\(=\frac{\sqrt{3}}{2}.\sqrt{1-a^2}+\frac{1}{2}.a=\frac{1}{2}\left(\sqrt{3\left(1-a^2\right)}+a\right)\)
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