document.write( "Question 851970: 4 sin 2t − 2 tan 2t = 0 \n" ); document.write( "
Algebra.Com's Answer #513043 by DrBeeee(684)\"\" \"About 
You can put this solution on YOUR website!
Given;
\n" ); document.write( "(1) 4sin(2t) - 2tan(2t) = 0 or
\n" ); document.write( "(2) 4sin(2t) = 2tan(2t) or
\n" ); document.write( "(3) 2sin(2t) = tan(2t)
\n" ); document.write( "Since
\n" ); document.write( "(4) tan(x) = sin(x)/cos(x) we have
\n" ); document.write( "(5) 2sin(2t) = sin(2t)/cos(2t) or
\n" ); document.write( "(6) 2cos(2t) = 1 or
\n" ); document.write( "(7) cos(2t) = 1/2
\n" ); document.write( "Using the inverse of cosine we have
\n" ); document.write( "(8) 2t = arccos(1/2)
\n" ); document.write( "Use your scientific calculator to solve (8) for
\n" ); document.write( "(9) 2t = 60 or
\n" ); document.write( "(10) t = 30
\n" ); document.write( "Let's check this using (1).
\n" ); document.write( "Is (4sin(2*30) - 2tan(2*30) = 0)?
\n" ); document.write( "Is (4sin(60) - 2tan(60) = 0)?
\n" ); document.write( "Is (4*sqrt(3)/2 - 2*sqrt(3) = 0)?
\n" ); document.write( "Is (2*sqrt(3) - 2*sqrt(3) = 0)?
\n" ); document.write( "Is (0 = 0)? Yes
\n" ); document.write( "Answer: t = 30 degrees.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );