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Trig Functions question

by mjbc
Tags: functions, trig
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mjbc
#1
Apr9-07, 11:29 AM
P: 4
1. The problem statement, all variables and given/known data

Simplify: cosx / (1+sinx)

2. The attempt at a solution

1 / (sec x)(1+sin x)

1 / (sec x + (sin x / cos x))

1 / (sec x + tan x)

I know that the answer is sec x - tan x but don't know how to get there.

Any help would be appreciated.
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jing
#2
Apr9-07, 11:42 AM
P: 123
Do you know what the value of [tex]sec^2x-tan^2x[/tex] is?

The difference of two squares helps too.
mjbc
#3
Apr9-07, 11:49 AM
P: 4
sec^2 (x) - tan^2 (x) = 1

but nothing's squared in the problem

jing
#4
Apr9-07, 11:53 AM
P: 123
Trig Functions question

Not until you do some multiplying.

Do you understand what I mean by the difference of two squares?
Dick
#5
Apr9-07, 11:57 AM
Sci Advisor
HW Helper
Thanks
P: 25,228
You could also just multiply top and bottom of your given expression by (1-sin(x)) and expand. It's really the same thing as jing is suggesting.
mjbc
#6
Apr9-07, 12:01 PM
P: 4
OK, So it's

(sec x - tan x) / (sec x + tan x)(sec x -tan x)

= (sec x - tan x) / 1

= sec x -tan x

Thank you so much!!


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