# trig-reply to Reiny

posted by .

RE:
(- sin (x/2) /( 2 sin (x/2) + cos (x/2))

is an alternate representation for,

1 / ( 4 tan (x/2) + 2 )

Thanks for your help, sorry I posted 3 times, I thought you didn't understand what I needed. I really do appreciate your time spent.

just for your FYI, if you are interested, see towards the bottom of the link, before the plot, where it says they are equivalent. I guess Wolframe Alpha is wrong... huh, I couldn't quite get it and I'm sure you know more than I.

Arg, It won't let me post a link. Oh well, sorry and thanks again.

• trig-reply to Reiny -

I'm new to this. I didn't know you could reply to the original post? (testing with this reply), otherwise I would not have kept re-posting as a 'new' question.

I just noticed some replies as I was reading other questions. again, my apologies. I feel like I should change my name if I have another question! have a good night.
Carol

• trig-reply to Reiny -

Since we did not resolve your question, I am curious where you got this problem.
Is it from a textbook?
Is in an assignment problem?
Just curious, since it obviously not a true statement.

• trig-reply to Reiny -

It's actually the end of an integration problem from a college calc text I have from 1971. The problem involved Weierstrass Substitution. The part I posted was after converting from the u-substition to an answer in terms of x.
The orig prob. is
integrate (cos x )/(3 cos^2 x - 5 cos x - 4 sin x cos x ) dx
I'll paste the part I was referring to in a new reply post.

• trig-reply to Reiny -

Continued, also this isn't an official assignment. I'm teaching myself calculus. I just love math. I took cal 30 thirty ago but don't remember much.
I use Wolframe Alpha to check my answers.
here's the web paste without the beg. address part, you'll have to copy and paste. look at the bottom just before the graph.

wolframalpha dotcom period slash input/?i=integrate+%28cos+x++%29%2f%283+cos^2+x+-+5+cos+x+-+4+sin+x+cos+x+%29++dx&asynchronous=pod&s=29&incTime=true

• trig-reply to Reiny -

I did manage to cut and paste your link, here is what I found:
http://www.wolframalpha.com./input/?i=integrate+%28cos+x++%29%2f%283+cos^2+x+-+5+cos+x+-+4+sin+x+cos+x+%29++dx&asynchronous=pod&s=29&incTime=true

I did notice that the equivalence was between

-sin(x/2)/(2sin(x/2) + cos(x/2)) and
- 1/(cot(x/2) + 2)
which is different from what you had.

as I said it my first reply to an earlier post, since all angles are x/2 , for convenience I will use Ø for x/2

so let's prove
-sinØ/(2sinØ + cosØ) = -1/(cotØ + 2)

RS = -1/(cosØ/sinØ + 2)
= -1/((cosØ + 2sinØ)/sinØ)
= =sinØ/(2sinØ + cosØ) , I multiplied by the reciprocal
= LS

OK then!!!! We got it.

Btw, good for you to work on this all by yourself.
Looks like you have reached quite an advanced stage already.

• trig-reply to Reiny -

sorry for the late thank you!!

I lost the post and couldn't find it.

doubt you will see this, and I didn't want to clog up the page with a new post.

you're the greatest!!

## Similar Questions

1. ### Trig

Given: cos u = 3/5; 0 < u < pi/2 cos v = 5/13; 3pi/2 < v < 2pi Find: sin (v + u) cos (v - u) tan (v + u) First compute or list the cosine and sine of both u and v. Then use the combination rules sin (v + u) = sin u cos …

3. ### Trig.......

I need to prove that the following is true. Thanks (2tanx /1-tan^x)+(1/2cos^2x-1)= (cosx+sinx)/(cosx - sinx) and thanks ........... check your typing. I tried 30º, the two sides are not equal, they differ by 1 oh , thank you Mr Reiny …
4. ### Mathematics - Trigonometric Identities

Let y represent theta Prove: 1 + 1/tan^2y = 1/sin^2y My Answer: LS: = 1 + 1/tan^2y = (sin^2y + cos^2y) + 1 /(sin^2y/cos^2y) = (sin^2y + cos^2y) + 1 x (cos^2y/sin^2y) = (sin^2y + cos^2y) + (sin^2y + cos^2y) (cos^2y/sin^2y) = (sin^2y …
5. ### TRIG!

Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6 x=1 - (3/4)sin^2 2x work on one side only! Responses Trig please help! - Reiny, Monday, February 23, 2009 at 4:27pm LS looks like the sum of cubes sin^6 x + cos^6 …
6. ### Trig.

tan^2BeatacscBeta-tan^2 (simplify) (sin/cos)^2Beta times 1/sin-(sin/cos)^2 (sin^2/cos^2)-(sin^2/cos^2)=-sin/cos Is this correct?
7. ### trig 26

simplify to a constant or trig func. 1. sec ²u-tan ²u/cos ²v+sin ²v change expression to only sines and cosines. then to a basic trig function. 2. sin(theta) - tan(theta)*cos(theta)+ cos(pi/2 - theta) 3. (sec y - tan y)(sec y + …
8. ### trig

I asked below but I guess it was not understood what I was asking. I'll try again. Could someone show me how, (- sin (x/2) /( 2 sin (x/2) + cos (x/2)) is an alternate representation for, 1 / ( 4 tan (x/2) + 2 ) TIA Carol I know the …
9. ### trig

Third time is the charm? I'll try again. Could someone show me how, (- sin (x/2) /( 2 sin (x/2) + cos (x/2)) is an alternate representation for, 1 / ( 4 tan (x/2) + 2 ) TIA Carol This doesn't require the solving of any equations. For
10. ### precalculus

For each of the following determine whether or not it is an identity and prove your result. a. cos(x)sec(x)-sin^2(x)=cos^2(x) b. tan(x+(pi/4))= (tan(x)+1)/(1-tan(x)) c. (cos(x+y))/(cos(x-y))= (1-tan(x)tan(y))/(1+tan(x)tan(y)) d. (tan(x)+sin(x))/(1+cos(x))=tan(x) …

More Similar Questions