document.write( "Question 1003087: Use trigonometric identities to solve tan(2θ)+tan(θ)=0 exactly for 0≤θ≤π. \n" ); document.write( "
Algebra.Com's Answer #619946 by Alan3354(69443)\"\" \"About 
You can put this solution on YOUR website!
Use trigonometric identities to solve tan(2x)+tan(x)=0 exactly
\n" ); document.write( "-----------
\n" ); document.write( "tan(2x) = 2tan(x)/(1 - tan^2(x))
\n" ); document.write( "--> 2tan(x)/(1 - tan^2(x)) + tan(x) = 0
\n" ); document.write( "tan(x) = 0
\n" ); document.write( "--> x = 0, pi
\n" ); document.write( "=========================
\n" ); document.write( "2/(1 - tan^2(x)) + 1 = 0
\n" ); document.write( "2/(1 - tan^2(x)) = -1
\n" ); document.write( "(1 - tan^2(x))/2 = -1
\n" ); document.write( "1 - tan^2(x) = -2
\n" ); document.write( "tan^2(x) = 3
\n" ); document.write( "x = sqrt(3)
\n" ); document.write( "--> x = pi/3, 4pi/3
\n" ); document.write( "-----
\n" ); document.write( "x = -sqrt(3)
\n" ); document.write( "--> x = 2pi/3, 5pi/3
\n" ); document.write( "------------------------------------------
\n" ); document.write( "That's theta from 0 to 2pi. If you only want up to pi eliminate the others. \n" ); document.write( "
\n" );