Question

Find all solutions in the interval [0, 2π).

tan x + sec x = 1

Answer 1

@Mertsj

Answer 2

Change everything to sine and cosine

Answer 3

im not sure how to do that @Mertsj

Answer 4

What is the definition of tangent?

Answer 5

opposite/adjacent

Answer 6

In terms of sin and cosine?

Answer 7

sin x /cos x

Answer 8

yes. And what is sec?

Answer 9

1/cos x

Answer 10

Yes. So now we have:

Answer 11

sin x /cos x + 1/ cos x =1 ?

Answer 12

\[\frac{\sin x}{cosx}+\frac{1}{\cos x}=1\]

Answer 13

So multiply each term by cos x

Answer 14

sinxcosx + cosx = cosx

Answer 15

@Mertsj

Answer 16

\[\frac{\sin x}{\cos x}\times cosx +\frac{1}\cos x \times \cos x=1\times \cos x\]

Answer 17

sin x + cos x = cos x ?

Answer 18

@Mertsj

Answer 19

sinx + 1 = cosx

Answer 20

now what do i do?

Answer 21

x =

x = 0

x =

No solution

Answer 22

x = π/4

x = 0

x = 5π/4

No solution

Answer 23

@Mertsj

Answer 24

no solution

Answer 25

thank u

Answer 26

No wait. I think that 0 might work.

Answer 27

Try it

Answer 28

i did. its 0. @Mertsj

Answer 29

Good.