Question

Calculate the value of the expression $4({\sin }^4{30}^{\circ }+{\cos }^4{30}^{\circ })-3({\cos }^2{45}^{\circ }-{\sin }^2{90}^{\circ })$

Answer 1

$4({\sin }^4{30}^{\circ }+{\cos }^4{30}^{\circ })-3({\cos }^2{45}^{\circ }-{\sin }^2{90}^{\circ })$

= $4\left(\right(\frac{1}{2}{)}^4+\left(\frac{\sqrt{3}}{2}{)}^4\right)-3\left(\right(\frac{1}{\sqrt{2}}{)}^2-\left(1{)}^2\right)$

= $4(\frac{1}{16}+\frac{9}{16})-3(\frac{1}{2}-1)$

= $4\left(\frac{10}{16}\right)+\frac{3}{2}$

= $\frac{5}{2}+\frac{3}{2}$
= $4$