Question

how do you solve this-
indefinite integration of(sin(x-a)/sin(x+a))^1/2

Answer 1

The whole thing is squarerooted, that makes sense haha. http://www.wolframalpha.com/input/?i=integrate+%28sin%28x-a%29%2Fsin%28x-a%29%29%5E%281%2F2%29

Answer 2

batman, you have a x -a in the denominator

Answer 3

ashgkasdhgasgkh

Answer 4

Yeah so it's something crazy

Answer 5

it doesnt looks like wolfram has a simple output
http://www.wolframalpha.com/input/?i=integrate+%28sin%28x-a%29%2Fsin%28x%2Ba%29%29^%281%2F2%29

Answer 6

woops i meant to say, double check your integral

Answer 7

Nope, I'm not exactly sure how I would approach this

Answer 8

its ok, i think we need more information from the original poster

Answer 9

wolfram is giving complex stuff because it is assuming x takes all real values

Answer 10

if it is a real valued function, we need to work it only when the ratio of sins inside the radical is nonnegative i think

Answer 11

x+a=/=npi, n E Z

Answer 12

sin(x-a) = sin(x+a)cos2a-cos(x+a)sin2a
sin(x+a) = cos2a-sin2a*cot(x+a)

integrate idk

Answer 13

sin(A+B)=sin A cos B + cos A sin B

Answer 14

sin(A-B)==sin A cos -B + cos A sin -B
=sinA cosB -CosA SinB

Answer 15

hmmm

Answer 16

now how about multipling by cojugate

Answer 17

if u want a feel for graph of function :

Answer 18

(sin A cos B + cos A sin B) (sin A cos B + cos A sin B)
----------------------------------------------
sin A cos B - cos A sin B(sin A cos B + cos A sin B)

Answer 19

is it possible to change this whole thing to complex form??

Answer 20

and take the imaginary part as solution

Answer 21

idk how we define area in complex

Answer 22

hey how about this thought

Answer 23

suppose i write
sin(x-a)
-------
sin(x+a)
in complex form, now there shud be 4 seperate expansions and we want to

Answer 24

oh you want to integrate real and imaginary parts separately and add up ?

Answer 25

only consider the part where that complex expressio nis dealing with the one above

Answer 26

and we know it must exist in the real part, however the teal part will also include the cos(x-a)/cos(x+a)

Answer 27

i think we need to assume the given funciton is complex valued

Answer 28

the complex parst will be from
cos(x-a)
------
-sin(x+a)
and
isin(x-a)
--------
cos(x+a)

Answer 29

so we can rigt away eliminate the complex solution from our integral after we are done

Answer 30

since none of that contain the sin(x-a)/sin(x+a)

Answer 31

uhh nvm!

Answer 32

forgot there ssome real parts and im parts i dunnooo maybe ill work on it xD expand the whole thing and see if we can simplfy it somehow with complex

Answer 33

pretty sure its some trig sub stuff thoughhh

Answer 34

i really tried solving this, and dan815, i tried expanding sin(x+a) and sin(x-a) and solving, but that only makes a bigger mess of things.

Answer 35

the answer is:\[\cos a. arc \cos(\cos x \div \cos a)-\sin a.\ln(\sin x+\sqrt{\sin²x-\sin²a})+c\]