document.write( "Question 197454: Solve for x in the equation (1 +sinx/cosx)+(cosx/1+sinx)=4 for 0≤ x ≤ 2π rad. \n" ); document.write( "

Algebra.Com's Answer #160628 by HyperBrain(694) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"%281+%2Bsinx%29%2Fcosx+%2B+cosx%2F%281%2Bsinx%29=4\"$
\n" ); document.write( "Multiply both sides by cos x (1+ sin x)
\n" ); document.write( " $\"%281+%2B+sin+x%29%5E2+%2B+cos%5E2+%28x%29=4cos+x+%281%2B+sin+x%29\"$
\n" ); document.write( " $\"1%2B+2+sin+x+%2B+sin%5E2%28x%29+%2B+cos%5E2+%28x%29=4cos+x+%281%2B+sin+x%29\"$
\n" ); document.write( " $\"2%2B2sin+x=4cos+x%281%2Bsin+x%29\"$
\n" ); document.write( " $\"1%2B+sin+x=2cos+x%281%2Bsin+x%29\"$
\n" ); document.write( "Divide both sides by 1 + sin x
\n" ); document.write( " $\"2+cos+x=1\"$
\n" ); document.write( " $\"cos+x=1%2F2\"$
\n" ); document.write( "There are only two solutions:
\n" ); document.write( "x=pi/6 or 11pi/6 \n" ); document.write( "

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