Identities sin, cos, tan etc. stuff

  • #1

Homework Statement



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

Homework Equations




2012-03-05_12-13-36_59.jpg



The Attempt at a Solution



multiplied the left equation by (cos x)/(cos x) and the right fraction by (1+sin x)/(1+sin x)

get ((cosx)^2 +(1+sinx)^2) / (1+sinx) (cos x)

and I have no idea where to go from here
 
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Answers and Replies

  • #2
35,396
7,272

Homework Statement



((cos x)/(1+sin x))+((1+sin x)/(cos x))
What are you trying to do, simplify the expression above?

Homework Equations




2012-03-05_12-13-36_59.jpg



The Attempt at a Solution



multiplied the left equation by (cos x)/(cos x) and the right fraction by (1+sin x)/(1+sin x)

get ((cosx)^2 +(1+sinx)^2) / (1+sinx) (cos x)

and I have no idea where to go from here
 
  • #3
Yes, the answer being 2 sec x
 
  • #4
35,396
7,272
Expand the numerator and simplify.
((cosx)^2 +(1+sinx)^2) / (1+sinx) (cos x)
 
  • #5
(1-sinx^2) +1 + sinx +1 - sin x

(1- sinx^2) +2 / (1+sin x)(cos x)

I don't see how that helps
 
  • #6
35,396
7,272
Expand the numerator and simplify.
((cosx)^2 +(1+sinx)^2) / (1+sinx) (cos x)

(1-sinx^2) +1 + sinx +1 - sin x
The only thing you did that makes sense is replacing cos2(x) with 1 - sin2(x). I don't get what you did go go from (1 + sin(x))2 to 1 + sin(x) + 1 - sin(x).

(1- sinx^2) +2 / (1+sin x)(cos x)

I don't see how that helps
 
  • #7
Then what simplifying is there to do?
 
  • #8
35,396
7,272
Apparently I wasn't clear. (1 + sin(x))2 ≠ 1 + sin(x) + 1 - sin(x), which seems to be what you're saying.

The "simplifying" that you need to do is to expand (1 + sin(x))2 to something it is actually equal to.
 
  • #9
Okay it equals (1+sinx)(1-sinx)
still not way to get to 2secx
 
  • #10
35,396
7,272
Because that's wrong, too. (1 + sin(x))2 ≠ (1+sinx)(1-sinx), if that's what you're saying.

How do you expand (1 + x)2? This is a similar kind of problem.
 
  • #11
Okay it equals (1+sinx)(1+sinx)
still no way to get to 2secx
 
  • #12
22,129
3,298
Okay it equals (1+sinx)(1+sinx)

Expand the expression: apply distributivity to work out the brackets.
 
  • #13
All right got it
 

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