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 #854651 by ikleyn(53937)\"\" \"About 
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\n" ); document.write( "Solve for x in the equation (1 +sinx/cosx)+(cosx/1+sinx)=4 for 0≤ x ≤ 2π rad.
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\n" ); document.write( "\n" ); document.write( "        The answers x = pi/6 or 11pi/6 in the post by HyperBrain both are incorrect.\r
\n" ); document.write( "\n" ); document.write( "        I came to bring a correct solution.\r
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\n" ); document.write( "\n" ); document.write( "\"%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/3 or 5pi/3\r
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\n" ); document.write( "\n" ); document.write( "Solved correctly.\r
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