Question

Find the value of:
${\sin }^2{30}^o+{\cos }^2{30}^o$

Answer 1

${\sin }^2{30}^{\circ }+{\cos }^2{30}^{\circ }$ by substituting the values

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

$=\frac{1}{4}+\frac{3}{4}=\frac{1+3}{4}=\frac{4}{4}=1$

or using the identity ${\sin }^2\theta +{\cos }^2\theta =1$ we have ${\sin }^2{30}^{\circ }+{\cos }^2{30}^{\circ }=1$