document.write( "Question 1081140: Solve 2sinxtanx=5-(1/cosx) \n" ); document.write( "

Algebra.Com's Answer #695228 by Boreal(15235) $\"\"$ $\"About$

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2 sin x*(sin x/ cos x)=(5 cos x-1)/cos x
\n" ); document.write( "2 sin ^2 x=5 cos x-1
\n" ); document.write( "2(1-cos^2)x=5 cos x-1
\n" ); document.write( "2-2 cos^2 x=5 cos x -1
\n" ); document.write( "0=2cos^2x+5 cos x -3= (2 cos x-1)(cos x +3)=0
\n" ); document.write( "only one of those factors works, and it is when cos x=1/2
\n" ); document.write( "That is at pi/3 and 5 pi/3
\n" ); document.write( "Check
\n" ); document.write( "2*(sqrt(3)/2)* sqrt (3)=5-(1/(1/2))
\n" ); document.write( "3=3\r
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