Answer:
The value of x = 1
Step-by-step explanation:
Given
To determine
x = ?
Using the trigonometric ratio
cos Ф = adjacent / hypotenuse
here
Ф = 45°
adjacent of 45° = x
hypotenuse = √2
so substituting Ф = 45° adjacent = x and hypotenuse = √2 in the equation
cos Ф = adjacent / hypotenuse
[tex]\cos \left(45^{\circ \:}\right)=\frac{x}{\sqrt{2}}[/tex]
switch sides
[tex]\frac{x}{\sqrt{2}}=\cos \left(45^{\circ \:}\right)[/tex]
Multiply both sides by 2
[tex]\frac{2x}{\sqrt{2}}=2\cos \left(45^{\circ \:}\right)[/tex]
[tex]\sqrt{2}x=\sqrt{2}[/tex] ∵ [tex]\cos \left(45^{\circ \:}\right)=\frac{\sqrt{2}}{2}[/tex]
Divide both sides by √2
[tex]\frac{\sqrt{2}x}{\sqrt{2}}=\frac{\sqrt{2}}{\sqrt{2}}[/tex]
[tex]x=1[/tex]
Therefore, the value of x = 1
