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solve equation

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solve equation

i want to solve this equation but i cannot because it is so complex.
please help me now. Thanks!!!
1/((tanx)^2+(1+tanx)^2) + 1/((cotx)^2+(1+cotx)^2) + ((sinx+cosx)^4)/4 = (5+(sin2x)^3)/4

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.

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