Answer
2
Work Step by Step
Given expression is-
$(\sin 45^{\circ} + \cos 45^{\circ})^{2}$
= $(\sin 45^{\circ})^{2} + (\cos 45^{\circ})^{2} + 2 \sin 45^{\circ} \cos 45^{\circ} $
[Recall $ (a+b)^{2} = a^{2} + b^{2} + 2 a b $]
= $(\frac{1}{\sqrt 2})^{2} + (\frac{1}{\sqrt 2})^{2} + 2 . \frac{1}{\sqrt 2} . \frac{1}{\sqrt 2}$
(Substituting exact values)
= = $(\frac{1}{2}) + (\frac{1}{2}) $ + $1$
( As $\sqrt 2.\sqrt 2 = 2)$
= $1 + 1$ = 2
