Question about simplifying this equation

Main Question or Discussion Point

tan x/sin x + 1/cos x

The choices are A. 2tan^2x B. 2cosx C. 2cosx-1 D. 2secx

Do I make the tan sin/cos and multiply by reciprocal of sin? I did that and end up with 1/cos + 1/cos
 

Answers and Replies

mathman
Science Advisor
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tan x/sin x + 1/cos x

The choices are A. 2tan^2x B. 2cosx C. 2cosx-1 D. 2secx

Do I make the tan sin/cos and multiply by reciprocal of sin? I did that and end up with 1/cos + 1/cos
You got it right so far. Do you know what secx is?
 
441
0
Tan x / Sin x + 1 /cos x

Since tanx = (sinx/cosx) we can substitute and get:

(Sinx / cos x)/ Sin x + 1 / cos x

here we can cancel out the sin x 's and get

1 / cos x + 1 / cos x

since the denominators are the same we can add and get

2 / cos x

Now since sec x = 1 / cosx we get

2 sec x


Make sense?
 
Tan x / Sin x + 1 /cos x

Since tanx = (sinx/cosx) we can substitute and get:

(Sinx / cos x)/ Sin x + 1 / cos x

here we can cancel out the sin x 's and get

1 / cos x + 1 / cos x

since the denominators are the same we can add and get

2 / cos x

Now since sec x = 1 / cosx we get

2 sec x


Make sense?
Yeah, thanks for that. But I thought about what mathman said and the answer was obvious, lol. Thanks a lot though for working it out.

You got it right so far. Do you know what secx is?
Yeah, so the 2(1/cosx) becomes 2secx...

That was pretty stupid, lol. Thanks though. This is a little off-topic for this thread but I really lack in courses like physics and math and I really like this forum (I'm new, lol) and what I like is how you guys don't just give an answer. You either show all the steps like Diffy did or what you did and made me think about it. :)
 
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I have another question I can't understand.

Which expression is equivalent to cos(pi + theta) (I don't know how to import the signs. and I checked the computer's character map)

So what I did was take cos(pi + theta) and put down the formula:

cos pi * cos theta - sin pi * sin theta

But I don't know what to do from there. I tried to see if I could do anything putting sin over cos but they're on opposite sides of the "-".

Choices are: A. -cos theta B. cos theta C. -sin theta D. sin theta
 
441
0
you have cos(pi) and Sin(pi) in your expressions... What is the cos(pi)? sin(pi)?
 
441
0
you have cos(pi) and Sin(pi) in your expressions... What is the cos(pi)? sin(pi)?
Thanks for telling me about the symbols. That should come in handy :)


Just realized this isn't the forum for homework questions so I'm going to make a new thread in the correct section.
 
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