Question

Find the value of $({\sin }^2{30}^{\circ }+{\cos }^2{30}^{\circ }+{\cot }^2{45}^{\circ })$

Answer 1

${\sin }^2{30}^{\circ }+{\cos }^2{30}^{\circ }+{\cot }^2{45}^{\circ }$
= $(\frac{1}{2}{)}^2+(\frac{\sqrt{3}}{2}{)}^2+1^2$
= $\frac{1}{4}+\frac{3}{4}+1$
= $\frac{1+3+4}{4}$
= $\frac{8}{4}$
= $2$