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 2 years ago
Let f(x) = sin(x) + icos(x). Show that f(x) = 1.
I'm not even sure where to start here...
 2 years ago
Let f(x) = sin(x) + icos(x). Show that f(x) = 1. I'm not even sure where to start here...

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khurramshahzad
 2 years ago
Best ResponseYou've already chosen the best response.0hey its too much easy... f(x)=sqrt((1)^2+(1)^2)=sqrt(2)

khurramshahzad
 2 years ago
Best ResponseYou've already chosen the best response.0here we will take its real part 1 will cos(x) and also 1 from imagnary part i(sinx) hey u have written wrong equation.. its cos(x)isin(x)

thrustfault
 2 years ago
Best ResponseYou've already chosen the best response.0The question is right. I know DeMoivres, but in this case it's sin(x) + icos(x).

khurramshahzad
 2 years ago
Best ResponseYou've already chosen the best response.0ah oookkk ya its absolute value

thrustfault
 2 years ago
Best ResponseYou've already chosen the best response.0So far I have LHS = \[\frac{ e ^{ix}e^{ix} }{ 2 } + \frac{ e ^{ix}+e^{ix} }{ 2 }i\] Have I completely overthought the problem ? :)

khurramshahzad
 2 years ago
Best ResponseYou've already chosen the best response.0no i is denominator from demorvie`s, but in this case I did`nt get u how u got this result

khurramshahzad
 2 years ago
Best ResponseYou've already chosen the best response.0ok am gonna solve its prove and implement according to this condition the `ll msg u here ok

thrustfault
 2 years ago
Best ResponseYou've already chosen the best response.0Thanks :) I'm so confused...

khurramshahzad
 2 years ago
Best ResponseYou've already chosen the best response.0hahahhah i just wanna say write i in denominator ok i mean (eix−e−ix)2+(eix+e−ix)2i

thrustfault
 2 years ago
Best ResponseYou've already chosen the best response.0Hmm... I don't get it. How does that show that sin(x) + icos(x) = 1?

khurramshahzad
 2 years ago
Best ResponseYou've already chosen the best response.0oh i see wait i solve it and post the diagrame okk buddy

khurramshahzad
 2 years ago
Best ResponseYou've already chosen the best response.0daer i can`t .. i have seen the same result for it sqareroot 2 iz answer for both condition.. cos when we see cosx+isinx,, or sinx+icosx... taking coifficients we get the same result..

khurramshahzad
 2 years ago
Best ResponseYou've already chosen the best response.0i thinks its wrong question or some thing missing ... can u give the link where did u got it from ???

thrustfault
 2 years ago
Best ResponseYou've already chosen the best response.0Yep, it's question 1 iv) from this paper: http://www.scribd.com/doc/112148611/MATH1131Mathematics1A1 Thanks :)

khurramshahzad
 2 years ago
Best ResponseYou've already chosen the best response.0http://www.mathwarehouse.com/ellipse/equationofellipse.php http://www.algebra.com/algebra/homework/equations/THEO20100329.lesson

khurramshahzad
 2 years ago
Best ResponseYou've already chosen the best response.0u got ur answer or not /??

thrustfault
 2 years ago
Best ResponseYou've already chosen the best response.0Nope, heh. Not yet :(

khurramshahzad
 2 years ago
Best ResponseYou've already chosen the best response.0ok if its difficault then msg me ur question i will solve it my self and will post the pic here ok

thrustfault
 2 years ago
Best ResponseYou've already chosen the best response.0Yeah I don't know how to get the function to = 1...

AccessDenied
 2 years ago
Best ResponseYou've already chosen the best response.1I am thinking that you are using the fact that f(x) represents the exact distance between it and 0 on the complex plane... Notice that you can create a right triangle with the real part of f(x) and the imaginary part of x on a complex plane: dw:1352104120632:dw So, here, Re(f) = sin(x) and Im(f) = cos(x). We drop off the i since we're dealing with distances only for the imaginary part. Using Pythagorean theorem, f(x)^2 = (Re(f))^2 + (Im(f))^2 = sin^2 x + cos^2 x. Since we have a neat trigonometric identity here, we can use it to reduce sin^2 x + cos^2 x as 1. Take the square root of both sides and we're done. :)

thrustfault
 2 years ago
Best ResponseYou've already chosen the best response.0Thanks so much for your clear and concise answer!! I've been stuck on this question for a long time :)

AccessDenied
 2 years ago
Best ResponseYou've already chosen the best response.1You're welcome! :)

sirm3d
 2 years ago
Best ResponseYou've already chosen the best response.1perhaps this definition can refresh you \[\huge \left a + bi \right=a^2+b^2 \]
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