If 3sec^2 x  - 4 = 0  find x value

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hala718 | High School Teacher | (Level 1) Educator Emeritus

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If 3sec^2 x  - 4 = 0

First we will add 4 to both sides:

==> 3sex^2 x = 4

Now divide by 3:

==> sec^2 x = 4/3

Now we will apply the square root for both sides:

==> sec x = sqrt(4/3)

==> secx = sqrt4/ sqrt3

==> secx = 2/sqrt3

But we know that:

secx = 1/cosx

==> (1/cosx ) = 2/sqrt3

==> cosx = sqrt3/2

The angle whose cosine is sqrt3/2 is pi/6

Since the angle is positive, then the angle is located in the first and fourth quadrants:

==> x1=  pi/6

==> x2= (2pi - pi/6) = 11pi/6

Then the answer is:

x = { pi/6 , 11pi/6}

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