Question

Solve the equation 2 cos X - sec x = 1 on the interval [0,2pi)

Answer 1

Step 1: Change sec x = 1/cos x (as sec x and cos x are receiprocals of each other).

Answer 2

Tell me when you did that.

Answer 3

done

Answer 4

Step 2: Multiply both sides of the equation by cos x. (This will get rid of the fraction's denominator on the left side). Tell me when you have done that.

Answer 5

done

Answer 6

what do you have as your equation now?

Answer 7

2 cos^2 x - 1 = cos x

Answer 8

You should have: 2 cos^2 (x) - 1 = cos x

Answer 9

yes

Answer 10

Subtract cos x from both sides...we have a quadratic equation...

so you have 2 cos^2(x) - cos x - 1 = 0

Answer 11

We will now factor that quadratic equation:
(2 cos x + 1)(cos x - 1) = 0

Answer 12

Tell me when you clearly understand everything till this point.

Answer 13

yes

Answer 14

We now set each factor equal to 0:

2 cos x + 1 = 0
2 cos x = -1
cos x = -1/2


cos x - 1 = 0
cos x = 1

Answer 15

now you dind the angles.

Answer 16

-pi/6 only?

Answer 17

cos x = 1 at x = 0

Answer 18

cos x = -1/2 at 2pi/3 and 4pi/3

Answer 19

3 solutions