Question

sin square 30 degree cos square 45 degree + 4 tan square 30 degree + half sin square 90 degree-2 cos square 90 degree + 1 divided by 24 cos square 0 degree

Answer 1

$$\begin{gathered} \frac{{\sin }^{2}30{\cos }^{2}45+4{\tan }^{2}30+{\displaystyle \frac{1}{2}}{\sin }^{2}90-2{\cos }^{2}90+1}{24{\cos }^{2}0} \\ =\frac{{\left({\displaystyle \frac{1}{2}}\right)}^2{\left({\displaystyle \frac{1}{\sqrt{2}}}\right)}^2+4{\left({\displaystyle \frac{1}{\sqrt{3}}}\right)}^2+\left({\displaystyle \frac{1}{2}}\right)\left(1\right)-0+1}{24} \\ =\frac{{\displaystyle \frac{1}{8}}+{\displaystyle \frac{4}{3}}+{\displaystyle \frac{1}{2}}+1}{24} \\ =\frac{{\displaystyle \frac{3+32+12+24}{24}}}{24}=\frac{71}{576}\mathrm{ANS}... \end{gathered}$$