Question

Pi/24 is the solution for 4cos2 (4x) - 3 = 0

True or false

Answer 1

True statement

Step-by-step explanation:

Given the equation,
`4cos^2 (4x)-3`= 0

On solving,

`4 \cos ^(2)(4 x)=3`

`\cos ^(2)(4 x)=(3)/(4)`

Taking square root both sides

We get,

`\cos 4 x=(√(3))/(2)`

`(√(3))/(2)=\cos (\pi)/(6)`

Putting it in the equation

`\cos 4 x=\cos (\pi)/(6)`

`4 x=(\pi)/(6)`

x = π/24

Answer 2

True.

Step-by-step explanation:

Given,

4cos2 (4x) - 3 = 0

Now, 4π/24 = π/6

Or, cos π/6 = √3/2

Or, cos^2 π/6 = 3/4

Or, 4 cos^2 π/6 = 3

Now, Left Hand Side= 4cos2 (4x) - 3

= 3-3 =0 = Right Hand Side (Proved)

Here, Left Hand Side= Right Hanad Side. So, 4cos2 (4x) - 3=0 is true.