document.write( "Question 615760: find all the solution of the equation in the interval (0,2pi) \r
\n" ); document.write( "\n" ); document.write( "tan(x+pi)+2 sin(x+pi)=0 \n" ); document.write( "

Algebra.Com's Answer #387368 by lwsshak3(11628) $\"\"$ $\"About$

You can put this solution on YOUR website!
find all the solution of the equation in the interval (0,2pi)
\n" ); document.write( "tan(x+pi)+2 sin(x+pi)=0
\n" ); document.write( "tan(x+π)/sin(x+π)=-2
\n" ); document.write( "[sin(x+π)/cos(x+π)]/sin(x+π)=-2
\n" ); document.write( "sin(x+π) cancels out
\n" ); document.write( "1/cos(x+π)=-2
\n" ); document.write( "cos(x+π)=-1/2
\n" ); document.write( "x+π=2π/3 and 4π/3 (in quadrants II and III where cos<0)
\n" ); document.write( "x+π=2π/3
\n" ); document.write( "x=2π/3-π=-π/3
\n" ); document.write( "and
\n" ); document.write( "x+π=4π/3
\n" ); document.write( "x=4π/3-π=π/3
\n" ); document.write( "ans:
\n" ); document.write( "x=-π/3 and π/3
\n" ); document.write( " \n" ); document.write( "

\n" );