Question

Which of the following is equivalent to the expression below?
1+sec(theta)
-----------------
tan(theta)+sin(theta)

Answer 1

\[\frac{1 + sec(\theta)}{tan(\theta) + sin(\theta)} = \frac{1 + \frac{1}{cos(\theta)}}{\frac{sin(\theta)}{cos(\theta)} + sin(\theta)}\]

Answer 2

I dunno what options you have, these trig identities can get complicated.

Answer 3

csc(theta)
tan(theta)
-1
sec(theta)
cot(theta)

Answer 4

Well, from the denominator you can factor out a sin(theta) from each term.. what do you have then?

Answer 5

uh (1+1/cos(theta))/(cos(theta))?

Answer 6

no. try factoring again

\[\frac{sin\theta}{cos\theta} + sin\theta = ?\]

Answer 7

sec(theta)

Answer 8

that's the answer yes, but not what I was asking.. I assume you saw the solution after you factored it?

Answer 9

err actually no, that's not the answer. nvm

Answer 10

what do you get when you factor out a sin(theta) from that expression in the denominator?

Answer 11

uhhhh ok how do I factor it out?

Answer 12

How do you factor out the a from 2a + ba ?

Answer 13

Or factor out a 2 from (4 + 6a)

Answer 14

sin(theta)(1/cos(theta)

Answer 15

close

Answer 16

try this one:

factor completely (10x+2)

Answer 17

2(5x+1)

Answer 18

right.

Now try \(\frac{a}{b} + a\)

Answer 19

or we can write it as\[\frac{1}{b}*a + a\]

Answer 20

if that makes it clearer

Answer 21

sin(θ)(1+cos(θ))/cos(θ)

Answer 22

no.

Answer 23

\[\frac{a}{b} + a = a(\frac{1}{b} + 1). a = sin(\theta), b = cos(\theta) \]\[\implies \frac{sin(\theta)}{cos(\theta)} + sin(\theta) = sin\theta(\frac{1}{cos\theta} + 1)\]

Answer 24

oh ok.... i guess i was kinda close, but not really

Answer 25

so from there you should see something nice to cancel and get a simple answer

Answer 26

what like the 1?

Answer 27

no

Answer 28

Like the [1 + 1/cos(theta)] you have on top and bottom

Answer 29

what equation are you looking at?

Answer 30

\[\frac{1+\frac{1}{cos\theta}}{sin\theta (1 + \frac{1}{cos\theta})}\]

Answer 31

so all I have left is 1/sin(theta)?

Answer 32

indeed

Answer 33

which equals...csc(theta)

Answer 34

indeed

Answer 35

wow sorry about making that so difficult thank you so much!

Answer 36

lol, np