Answer:
[tex] \frac{\pi}{4} = 45° \\ \\ \frac{\pi}{6} = 30°[/tex]
[tex]( \cos( \frac{\pi}{4} ) + \sin( \frac{\pi}{6} ) ) ^{2} \\ \\ \\ {( \cos(45°) + \sin(30°) ) }^{2} \\ \\ \\ ( \frac{1}{ \sqrt{2} } + \frac{1}{2} ) ^{2} \\ \\ \\ (( \frac{1}{ \sqrt{2}} \times \frac{ \sqrt{2} }{ \sqrt{2}} ) + \frac{1}{2} )^{2} \\ \\ ( \frac{ \sqrt{2} }{2} + \frac{1}{2} )^{2} \\ \\ {( \frac{ \sqrt{2} + 1}{2} })^{2} \\ \\ \frac{( \sqrt{2} + 1)( \sqrt{2} + 1)}{ {2}^{2} } \\ \\ \\ \frac{2 + \sqrt{2} + \sqrt{2} + 1}{4} \\ \\ \\ = \frac{3 + 2 \sqrt{2} }{4} \\ \\ \\ = \frac{3 + 2(1.414)}{4} \\ \\ = \frac{3 + 2.828}{4} \\ \\ = \frac{5.828}{4} \\ \\ = 1.457[/tex]
I hope I helped you^_^
