Question

Evaluate$\sin 45°+\cos 45°$

Answer 1

Evaluating the given expression:

Given:$\sin 45°+\cos 45°$

With the help of a trigonometric table $\sin 45°=\frac{1}{\sqrt{2}}$ & $\cos 45°=\frac{1}{\sqrt{2}}$

So,$\sin 45°+\cos 45°=$$\frac{1}{\sqrt{2}}$$+$$\frac{1}{\sqrt{2}}$

$=$$\frac{1+1}{\sqrt{2}}$

$=$$\frac{2}{\sqrt{2}}$

$=$$\frac{2}{\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}}$ (Rationalizing the denominator)

$=$$\frac{2\sqrt{2}}{2}$

$=$$\sqrt{2}$

Thus, the required value of $\sin 45°+\cos 45°$ $\sqrt{2}$