Question

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

Answer 1

Answer:

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.

Answer 2

Answer:

True  statement

Explanation:

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

On solving,

$4 \cos ^{2}(4 x)=3$

$\cos ^{2}(4 x)=\frac{3}{4}$

Taking square root both sides

We get,

$\cos 4 x=\frac{\sqrt{3}}{2}$

$\frac{\sqrt{3}}{2}=\cos \frac{\pi}{6}$

Putting it in the equation

$\cos 4 x=\cos \frac{\pi}{6}$

$4 x=\frac{\pi}{6}$

x = π/24