Question

can someone help me why sin 45 + cos 45 = √2?

Answer 1

well using an exact ratio

\[\sin(45) = \cos(45) = \frac{1}{\sqrt{2}}\]

so then

\[\sin(45) + \cos(45) = \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}} = \frac{2}{\sqrt{2}}\]

the denominator has been rationalised..

\[\frac{2}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{2\sqrt{2}}{2}\]

hope this makes sense.

Answer 2

okay iwas staring at this for 3 minutes but i still didn't get it >< im so sorry. isnt cos and sin 45 = √2/2 ?

Answer 3

nope its

\[\frac{2}{\sqrt{2}}\]

Answer 4

from the exact value triangles