Question

Evaluate $si{n}^2{45}^{\circ }+{\tan }^2{45}^{\circ }+{\cos }^2{45}^{\circ }$

Answer 1

We know, $\sin {45}^{\circ }=\frac{1}{\sqrt{2}},\tan {45}^{\circ }=1$ and $\cos {45}^{\circ }=\frac{1}{\sqrt{2}}$
$\therefore {\sin }^2{45}^{\circ }+{\tan }^2{45}^{\circ }+{\cos }^2{45}^{\circ }={\left(\frac{1}{\sqrt{2}}\right)}^2+(1{)}^2+{\left(\frac{1}{\sqrt{2}}\right)}^2$
$=\frac{1}{2}+1+\frac{1}{2}=2$