Question

Solve the multiple-angle equation in the interval [0, 2π):
sec2x = 2

Answer 1

\[
\cos(2 x) =\frac 1 {\sec (2x)}=\frac 1 2
\]
Finish it from here

Answer 2

are u talking to the asker?

Answer 3

Yes

Answer 4

ok

Answer 5

What angle has cosine 1/2 in your given interval?

Answer 6

My possible answers are
A. x = π/8, 7π/8, 9π/8, 15π/8
B. x = π/12, 5π/12, 13π/12, 17π/12
C. x = π/6, 5π/6, 7π/6, 11π/6
D. x = π/4, 3π/4, 5π/4, 7π/4
E. x = π/3, 2π/3, 4π/3, 5π/3

Answer 7

\[
\cos(2 x)=\frac 1 2\\
2 x = \pm \frac \pi 3 + 2 k \pi\\
x = \pm \frac \pi 6 + k \pi\\
\]
Which answer to choose from your choices?

Answer 8

Yeah. How do you get from what you just wrote to one of my options?

Answer 9

vary k over
\[
k=0,\, \pm 1, \, \pm2, \cdots

\]

Answer 10

you can take
\[
\frac \pi 6 + 0=\frac \pi 6\\
\frac \pi 6 +1 \pi=\frac {7\pi} 6\\
-\frac \pi 6 +1 \pi=\frac {5\pi} 6\\
-\frac \pi 6 +2 \pi=\frac {11\pi} 6\\
\]

Answer 11

Did you understand it?

Answer 12

Oooohh. Okay. Thanks for explaining. That was very helpful

Answer 13

yw