Question

$4({\sin }^4{30}^o+{\cos }^4{60}^o)-3({\cos }^4{45}^o-{\sin }^2{90}^o)$

Answer 1

$\begin{array}{c}4\left({\sin }^4{30}^{\circ }+{\cos }^4{60}^{\circ }\right)-3\left({\cos }^4{45}^{\circ }-{\sin }^2{90}^{\circ }\right)\\ \Rightarrow 4\left\{{\left(\frac{1}{2}\right)}^4+{\left(\frac{1}{2}\right)}^4\right\}-3\left\{{\left(\frac{1}{\sqrt{2}}\right)}^4-{\left(1\right)}^2\right\}\\ \Rightarrow 4\left\{\frac{1}{16}+\frac{1}{16}\right\}-3\left\{\frac{1}{4}-1\right\}\\ \Rightarrow 4\times \frac{2}{16}+\frac{9}{4}\\ \frac{1}{2}+\frac{9}{4}=\frac{11}{4}\end{array}$