4cos(θ)−2sec(θ)=0

Question

4cos(θ)−2sec(θ)=0

Answer 1

Le x = cosθ

 

Then

 

secθ = 1/cosθ = 1/x

 

4x - 2/x = 0

 

2x = 1/x

 

x² = 1/2

 

x = √(1/2) = (√2)/2

 

cosθ = (√2)/2

 

In radians, over [0,2π], θ = π/4 or 7π/4

Answer 2

FIRST, DIVIDE ALL TERMS BY 2.

Second, replace secant of theta by reciprocal of cosine.

Next, write 2 cos θ = 1/cos θ.

Now multiply each side by cosine of theta.

You should be able to proceed from there.

Answer 3

Let x=θ

 

Using the identity       secx = 1 / cosx

 

 

Then

 

4cosx - (2 / cosx) = 0

 

 

Multiply both sides of the equation by cosx.

 

4cos²x - 2cosx = 0

 

 

Factor out 2cosx.

 

2cosx(2cosx - 1) = 0

 

 

You can finish up from here.