Question

What is cos(45°)?

45°
1
Cos (459) = VI?
[]
COS
=
Hint: Remember to rationalize the denominator.

Answer 1

`\rm (\sqrt2)/(2)`

Explanation:

A right angled ∆ is given to us and we need to find out the value of cos 45° ( with rationalized denominator ) . As we know that in a right angle ∆ , the value of cosine is ,

`\rm\implies cos\theta =(base)/(hypotenuse)`

In the given triangle ,

• Value of base = 1
• Value of hypotenuse = √2

On substituting the respective values ,

`\rm\implies cos45^\circ =(1)/(\sqrt2)`

For rationalizing the denominator , multiply numerator and denominator by √2 , we have,

`\rm\implies cos45^\circ=(1(\sqrt2))/((\sqrt2)(\sqrt2))`

Simplify ,

`\rm\implies \boxed{\pink{\frak{ cos45^\circ=(\sqrt2)/(2) }}}`