document.write( "Question 1033152: He all,
\n" ); document.write( "I have some difficulties understanding the reason about the solution of this equation:
\n" ); document.write( "sin(x+π/3) = cos2x
\n" ); document.write( "proposed in the book, namely:
\n" ); document.write( "x= π/18+2kπ/3 V x= -π/6+2kπ
\n" ); document.write( "
\n" ); document.write( "My solution after converting to sin(x+π/3) = sin(π/2-2x) is:
\n" ); document.write( "x= π/18+kπ/9 V x= -π/6-kπ/3
\n" ); document.write( "Can somebody explain me step by step how to come to the
\n" ); document.write( "solution of the book?
\n" ); document.write( "Thank you very much in advance
\n" ); document.write( "RB
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #647809 by stanbon(75887) $\"\"$ $\"About$

You can put this solution on YOUR website!
sin(x+π/3) = cos2x
\n" ); document.write( "proposed in the book, namely:
\n" ); document.write( "x= π/18+2kπ/3 V x= -π/6+2kπ
\n" ); document.write( "-------
\n" ); document.write( "since sin(K) = cos((pi/2)-K) you can make a change on the left side::
\n" ); document.write( "cos((pi/2)-(x+(pi/3))) = cos(2x)
\n" ); document.write( "-----------
\n" ); document.write( "(pi/2)-x-(pi/3) = 2x
\n" ); document.write( "3x = [(3pi-2pi)/6]
\n" ); document.write( "----
\n" ); document.write( "x = pi/18 + 2kpi ; x = -pi/18 + 2kpi
\n" ); document.write( "----------------------------------------
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "

\n" );