solve equation

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# solve equation

Submitted by nona_nonomo on Fri, 11/26/2010 - 22:05

Forums:

i want to solve this equation but i cannot because it is so complex.

please help me now. Thanks!!!

equation:

1/((tanx)^2+(1+tanx)^2) + 1/((cotx)^2+(1+cotx)^2) + ((sinx+cosx)^4)/4 = (5+(sin2x)^3)/4

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## Versions

(v1) by nona_nonomo 2010-11-26

## Re: solve equation

Hi Nona,

The most you can do is to obtain a polynomial equation in terms of sin{2x} and its powers n = 0,1,2, ...

So convert your original Eq. in function of sines and cosines.

Recall that sin{2x} = 2.sin{x}.cos{x}, so sin^2{2x} = 4.sin^2{x}.cos^2{x}, and so on.

Eventually you will get terms like

cos^4{x} + sin^4{x} = (1 - sin^2{x})cos^2{x} + (1 - cos^2{x})sin^2{x}

= cos^2{x} + sin^2{x} - 2.sin^2{x}.cos^2{x} = 1 - (1/2)sin^2{2x}.

You must take care in your calculations because it are annoying.

perucho