anonymous
  • anonymous
Which of the following is equivalent to the expression below? 1+sec(theta) ----------------- tan(theta)+sin(theta)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[\frac{1 + sec(\theta)}{tan(\theta) + sin(\theta)} = \frac{1 + \frac{1}{cos(\theta)}}{\frac{sin(\theta)}{cos(\theta)} + sin(\theta)}\]
anonymous
  • anonymous
I dunno what options you have, these trig identities can get complicated.
anonymous
  • anonymous
csc(theta) tan(theta) -1 sec(theta) cot(theta)

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anonymous
  • anonymous
Well, from the denominator you can factor out a sin(theta) from each term.. what do you have then?
anonymous
  • anonymous
uh (1+1/cos(theta))/(cos(theta))?
anonymous
  • anonymous
no. try factoring again \[\frac{sin\theta}{cos\theta} + sin\theta = ?\]
anonymous
  • anonymous
sec(theta)
anonymous
  • anonymous
that's the answer yes, but not what I was asking.. I assume you saw the solution after you factored it?
anonymous
  • anonymous
err actually no, that's not the answer. nvm
anonymous
  • anonymous
what do you get when you factor out a sin(theta) from that expression in the denominator?
anonymous
  • anonymous
uhhhh ok how do I factor it out?
anonymous
  • anonymous
How do you factor out the a from 2a + ba ?
anonymous
  • anonymous
Or factor out a 2 from (4 + 6a)
anonymous
  • anonymous
sin(theta)(1/cos(theta)
anonymous
  • anonymous
close
anonymous
  • anonymous
try this one: factor completely (10x+2)
anonymous
  • anonymous
2(5x+1)
anonymous
  • anonymous
right. Now try \(\frac{a}{b} + a\)
anonymous
  • anonymous
or we can write it as\[\frac{1}{b}*a + a\]
anonymous
  • anonymous
if that makes it clearer
anonymous
  • anonymous
sin(θ)(1+cos(θ))/cos(θ)
anonymous
  • anonymous
no.
anonymous
  • anonymous
\[\frac{a}{b} + a = a(\frac{1}{b} + 1). a = sin(\theta), b = cos(\theta) \]\[\implies \frac{sin(\theta)}{cos(\theta)} + sin(\theta) = sin\theta(\frac{1}{cos\theta} + 1)\]
anonymous
  • anonymous
oh ok.... i guess i was kinda close, but not really
anonymous
  • anonymous
so from there you should see something nice to cancel and get a simple answer
anonymous
  • anonymous
what like the 1?
anonymous
  • anonymous
no
anonymous
  • anonymous
Like the [1 + 1/cos(theta)] you have on top and bottom
anonymous
  • anonymous
what equation are you looking at?
anonymous
  • anonymous
\[\frac{1+\frac{1}{cos\theta}}{sin\theta (1 + \frac{1}{cos\theta})}\]
anonymous
  • anonymous
so all I have left is 1/sin(theta)?
anonymous
  • anonymous
indeed
anonymous
  • anonymous
which equals...csc(theta)
anonymous
  • anonymous
indeed
anonymous
  • anonymous
wow sorry about making that so difficult thank you so much!
anonymous
  • anonymous
lol, np

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