Unable to use split. tryed doing with align got more error in that also due to this im unable to fit the equation the page

Question

\begin{eqnarray}
\begin{split}
  J_{cp} &=& \frac{1}{36} \bigg[\sqrt{3} \sin (2 \text{$\phi' $}) (\sin (\sigma ) \cos (\text{$\sigma' $}) \sin (2 \phi )-2 \sin (\text{$\sigma' $}) \cos (2 \phi ))\\
  &\quad-3 \sin (\sigma ) \sin (2 \phi ) \cos (2 \text{$\phi' $})\bigg]\\
  I_{1} &=& \frac{1}{288}\bigg[\left. 2 \sqrt{3} \sin (\phi) \sin (2 \phi') \left( 8 \sin (2 \sigma) \cos (\sigma') \sin (\phi) \cos^2 (\phi) \right. \right. \\
  &\quad \left. \left. + 2 \sin (\sigma') \left( 8 \cos (\sigma) \cos^3 (\phi) - 4 \cos (2 \sigma) \sin (\phi) \cos^2 (\phi) + \sin (\phi) + 5 \sin (3 \phi) \right) \right. \right.\\
  &\quad \left. \left. - 4 \sin (\sigma) \cos (\sigma') (\cos (\phi) + 3 \cos (3 \phi)) \right) \right. \\
  &\quad \left. + 6 \cos (2 \phi') \left( \sin (4 \phi) (\sin (\sigma - 2 \sigma') - 3 \sin (\sigma)) \right. \right. \\
  &\quad \left. \left. + \cos (\sigma') (-4 \sin (2 \phi) \sin (\sigma - \sigma') + 2 \sin (\sigma) \cos (4 \phi) \cos (\sigma - \sigma') \right. \right. \\
  &\quad \left. \left. - \sin (2 \sigma - \sigma') + 3 \sin (\sigma')) - 2 \sin (2 \sigma') \cos (2 \phi) \right) \right. \\
  &\quad \left. - 24 \sin (2 \sigma') \sin^3 (\phi) (2 \cos (\sigma) \cos (\phi) + \sin (\phi)) \right. \\
  &\quad \left. - 12 \sin (2 \phi) \left( \sin (\sigma) (\cos (2 \sigma') + 3) \cos (2 \phi) + \sin (\sigma') (\sin (2 \phi) \cos (2 \sigma - \sigma')\right) \right) \\
  &\quad  \left. + 2 \sin (\sigma) \sin (\sigma')  \right.\bigg]\\
  I_{2} &=& \frac{1}{2304} \bigg[\left. 96 \cos (2 \phi') \left( \sin^3 (\phi) \left( 8 \sin (\sigma) \cos^2 (2 \sigma') \cos (\phi) \right. \right. \right.\\
  &\quad \left. \left. + \sin (4 \sigma') (\sin (\phi) - 4 \cos (\sigma) \cos (\phi)) \right) \right. \\
  &\quad \left. - 2 \cos (2 \sigma') \sin^2 (2 \phi) \sin (2 (\sigma - \sigma')) \right) \\
  &\quad + 2 \sin (2 \sigma') \cos (4 \phi') \left( -24 \sin^3 (\phi) (\cos (2 \sigma') \sin (\phi) - 4 \cos (\phi) \cos (\sigma - 2 \sigma')) \right. \\
  &\quad \left. + 8 \sin (2 \phi) (\sin (2 \phi) (\cos (2 \sigma) - 3 \cos (2 (\sigma - \sigma'))) + \cos (\sigma)) \right. \\
  &\quad \left. - 36 \cos (\sigma) \sin (4 \phi) + 36 \cos (2 \phi) + 23 \cos (4 \phi) + 5 \right) \\
  &\quad + 64 \sqrt{3} \cos (2 \sigma') \sin (\phi) \sin (2 \phi') (2 \cos (\sigma) \sin (2 \phi) - 3 \cos (2 \phi) - 1) \\
  &\quad \left( 2 \sin (\sigma) \cos (\sigma') \cos (\phi) + \sin (\sigma') (\sin (\phi) - 2 \cos (\sigma) \cos (\phi)) \right) \\
  &\quad + 32 \sqrt{3} \sin (2 \sigma') \sin (\phi) \sin (4 \phi') (-2 \cos (\sigma) \sin (2 \phi) + 3 \cos (2 \phi) + 1) \\
  &\quad \left( \cos (\sigma') \sin (\phi) - 2 \cos (\phi) \cos (\sigma - \sigma') \right) \\
  &\quad - 288 \sin^2 (\sigma') \cos (\sigma') (\sin (4 \phi) \sin (\sigma - \sigma') + \sin (\sigma') \cos (2 \phi)) \\
  &\quad - 2 \sin (2 \sigma') (8 \sin (2 \phi) (\sin (2 \phi) (9 \cos (2 (\sigma - \sigma')) + \cos (2 \sigma)) \\
  &\quad - 9 \cos (\sigma - 2 \sigma') + \cos (\sigma)) + 9 \cos (2 \sigma') (\cos (4 \phi) + 3) + 23 \cos (4 \phi) + 5) \bigg] \\
\end{split}     
\end{eqnarray}

Answer 1

You never want to use eqnarray.

Removing all unnecessary \left and \right instructions and fixing the number of &, besides changing the incredibly wrong \text{$\phi'$} into \phi', I get a decent result.

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\begin{equation}
\begin{split}
  J_{cp} &= \frac{1}{36} \Bigl[\sqrt{3} \sin (2 \phi') (\sin (\sigma ) \cos (\sigma') \sin (2 \phi )-2 \sin (\sigma') \cos (2 \phi ))\\
  &\quad-3 \sin (\sigma ) \sin (2 \phi ) \cos (2 \phi')\Bigr]\\
  I_{1} &= \frac{1}{288}\Bigl[ 2 \sqrt{3} \sin (\phi) \sin (2 \phi') ( 8 \sin (2 \sigma) \cos (\sigma') \sin (\phi) \cos^2 (\phi)   \\
  &\quad   + 2 \sin (\sigma') ( 8 \cos (\sigma) \cos^3 (\phi) - 4 \cos (2 \sigma) \sin (\phi) \cos^2 (\phi) + \sin (\phi) + 5 \sin (3 \phi) )  \\
  &\quad   - 4 \sin (\sigma) \cos (\sigma') (\cos (\phi) + 3 \cos (3 \phi)) )  \\
  &\quad  + 6 \cos (2 \phi') ( \sin (4 \phi) (\sin (\sigma - 2 \sigma') - 3 \sin (\sigma))   \\
  &\quad   + \cos (\sigma') (-4 \sin (2 \phi) \sin (\sigma - \sigma') + 2 \sin (\sigma) \cos (4 \phi) \cos (\sigma - \sigma')   \\
  &\quad   - \sin (2 \sigma - \sigma') + 3 \sin (\sigma')) - 2 \sin (2 \sigma') \cos (2 \phi) )  \\
  &\quad  - 24 \sin (2 \sigma') \sin^3 (\phi) (2 \cos (\sigma) \cos (\phi) + \sin (\phi))  \\
  &\quad  - 12 \sin (2 \phi) ( \sin (\sigma) (\cos (2 \sigma') + 3) \cos (2 \phi) + \sin (\sigma') (\sin (2 \phi) \cos (2 \sigma - \sigma')) ) \\
  &\quad   + 2 \sin (\sigma) \sin (\sigma')  \Bigr]\\
  I_{2} &= \frac{1}{2304} \Bigl[ 96 \cos (2 \phi') ( \sin^3 (\phi) ( 8 \sin (\sigma) \cos^2 (2 \sigma') \cos (\phi)   \\
  &\quad   + \sin (4 \sigma') (\sin (\phi) - 4 \cos (\sigma) \cos (\phi)) )  \\
  &\quad  - 2 \cos (2 \sigma') \sin^2 (2 \phi) \sin (2 (\sigma - \sigma')) ) \\
  &\quad + 2 \sin (2 \sigma') \cos (4 \phi') ( -24 \sin^3 (\phi) (\cos (2 \sigma') \sin (\phi) - 4 \cos (\phi) \cos (\sigma - 2 \sigma'))  \\
  &\quad  + 8 \sin (2 \phi) (\sin (2 \phi) (\cos (2 \sigma) - 3 \cos (2 (\sigma - \sigma'))) + \cos (\sigma))  \\
  &\quad  - 36 \cos (\sigma) \sin (4 \phi) + 36 \cos (2 \phi) + 23 \cos (4 \phi) + 5 ) \\
  &\quad + 64 \sqrt{3} \cos (2 \sigma') \sin (\phi) \sin (2 \phi') (2 \cos (\sigma) \sin (2 \phi) - 3 \cos (2 \phi) - 1) \\
  &\quad ( 2 \sin (\sigma) \cos (\sigma') \cos (\phi) + \sin (\sigma') (\sin (\phi) - 2 \cos (\sigma) \cos (\phi)) ) \\
  &\quad + 32 \sqrt{3} \sin (2 \sigma') \sin (\phi) \sin (4 \phi') (-2 \cos (\sigma) \sin (2 \phi) + 3 \cos (2 \phi) + 1) \\
  &\quad ( \cos (\sigma') \sin (\phi) - 2 \cos (\phi) \cos (\sigma - \sigma') ) \\
  &\quad - 288 \sin^2 (\sigma') \cos (\sigma') (\sin (4 \phi) \sin (\sigma - \sigma') + \sin (\sigma') \cos (2 \phi)) \\
  &\quad - 2 \sin (2 \sigma') (8 \sin (2 \phi) (\sin (2 \phi) (9 \cos (2 (\sigma - \sigma')) + \cos (2 \sigma)) \\
  &\quad - 9 \cos (\sigma - 2 \sigma') + \cos (\sigma)) + 9 \cos (2 \sigma') (\cos (4 \phi) + 3) + 23 \cos (4 \phi) + 5) \Bigr] \\
\end{split}
\end{equation}

\end{document}

Answer 2

I suggest you switch to a single align* environment and be more circumspect about where you place the line breaks. I'd also get rid of all (yes, all) \left and \right sizing directives and get rid of most parentheses to declutter the appearance of the equations. And, don't be shy to use not only round parentheses but also square brackets and curly braces to provide some hierarchical visual structure on the expressions.

\documentclass{article} % or some other suitable document class
\usepackage[T1]{fontenc}
\usepackage{amsmath} % for 'align*' environment
\begin{document}

\begin{align*}
J_{cp} 
  &= \frac{1}{36} \bigl\{\sqrt{3} \sin 2\phi' (\sin\sigma  \cos\sigma' \sin 2\phi -2 \sin\sigma' \cos 2\phi ) \\
 &\qquad-3 \sin\sigma \sin 2\phi \cos 2\phi' \bigr\} \\[\jot]
I_{1} &= \frac{1}{288}\bigl\{ 2 \sqrt{3} \sin\phi \sin 2\phi' \bigl[ 8 \sin 2\sigma \cos\sigma' \sin\phi \cos^2\phi\\
 &\qquad\quad + 2 \sin\sigma' ( 8 \cos\sigma \cos^3\phi - 4 \cos 2\sigma \sin\phi \cos^2\phi + \sin\phi + 5 \sin 3\phi )\\
 &\qquad\quad - 4 \sin\sigma \cos\sigma' (\cos\phi + 3 \cos 3\phi) \bigr]\\
 &\qquad + 6 \cos 2\phi' \bigl[ \sin 4\phi (\sin(\sigma-2\sigma') - 3 \sin\sigma )
  + \cos\sigma' (-4 \sin 2\phi \sin (\sigma-\sigma')\\
 &\qquad\quad + 2 \sin\sigma \cos 4\phi \cos (\sigma-\sigma')
  - \sin (2 \sigma-\sigma') + 3 \sin\sigma') - 2 \sin 2\sigma' \cos 2\phi \bigr]\\
 &\qquad - 24 \sin 2\sigma' \sin^3\phi (2 \cos\sigma \cos\phi + \sin\phi)\\
 &\qquad - 12 \sin 2\phi \bigl[ \sin\sigma (\cos 2\sigma' + 3) \cos 2\phi \\
 &\qquad\quad + \sin\sigma' (\sin 2\phi \cos (2 \sigma-\sigma')) \bigr]
  + 2 \sin\sigma \sin\sigma' \bigr\} \\[\jot]
I_{2} &= \frac{1}{2304} \bigl\{ 96 \cos 2\phi'
\bigl[ \sin^3\phi ( 8 \sin\sigma \cos^2 2\sigma' \cos\phi + \sin 4\sigma' (\sin\phi - 4 \cos\sigma \cos\phi) )\\
   &\qquad\quad - 2 \cos 2\sigma' \sin^2 2\phi \sin (2 (\sigma-\sigma')) \bigr]\\
   &\qquad + 2 \sin 2\sigma' \cos 4\phi'
   \bigl[ -24 \sin^3\phi (\cos 2\sigma' \sin\phi - 4 \cos\phi \cos(\sigma-2\sigma'))\\
   &\qquad\quad +8 \sin 2\phi \bigl( \sin 2\phi [\cos 2\sigma - 3\cos(2 (\sigma-\sigma'))] + \cos\sigma \bigr) \\
   &\qquad\quad -36 \cos\sigma \sin 4\phi + 36 \cos 2\phi + 23 \cos 4\phi + 5 \bigr] \\
   &\qquad + 64 \sqrt{3} \cos 2\sigma' \sin\phi \sin 2\phi' (2 \cos\sigma \sin 2\phi - 3\cos 2\phi - 1) \\
   &\qquad\quad \times 4\sigma' \bigl( 2\sin\sigma \cos\sigma' \cos\phi + \sin\sigma' (\sin\phi-2\cos\sigma \cos\phi) \bigr) \\
   &\qquad + 32 \sqrt{3} \sin 2\sigma' \sin\phi \sin 4\phi' (-2 \cos\sigma \sin 2\phi + 3 \cos 2\phi + 1) \\
   &\qquad\quad \times 4\sigma' \bigl( \cos\sigma' \sin\phi - 2 \cos\phi \cos (\sigma-\sigma') \bigr) \\
   &\qquad - 288 \sin^2\sigma' \cos\sigma' (\sin 4\phi \sin (\sigma-\sigma') + \sin\sigma' \cos 2\phi ) \\
   &\qquad - 2 \sin 2\sigma' \bigl[8 \sin 2\phi (\sin 2\phi (9 \cos (2 (\sigma-\sigma')) + \cos 2\sigma) \\
   &\qquad\quad - 9 \cos(\sigma-2\sigma') + \cos\sigma ) + 9 \cos 2\sigma' (\cos 4\phi + 3) + 23 \cos 4\phi + 5 \bigr] \bigr\}
\end{align*}

\end{document}