Solution in radian

Question

2sec^2x + secx-1 =0

Answer 1

Factor your equation like a quadratic (just like 2x² + x - 1 = 0) to get:

 

(2secx - 1)(secx + 1) = 0

 

That means that 2secx - 1 = 0 or secx + 1 = 0.

 

 

First case:

 

2secx - 1 = 0

2secx = 1

secx = 1/2

1/cosx = 1/2

cosx = 2

 

This is impossible, as cosine never goes above a value of 1.

 

 

Second case:

 

secx + 1 = 0

secx = -1

1/cosx = -1

cosx = -1

 

Cosine is -1 at only one value in the unit circle: π. So, x = π radians.

 

 

The cosine function is periodic, so this cosine measure occurs every 2π radians. That is, π + 2π = 3π radians is a solution, as are 5π, 7π, 9π, etc. So, your total solution is:

 

x = π +2πn radians, where n is any integer.