document.write( "Question 1086461: Prove that sin x+ cos x =sqrt(2)sin(x+pi/4)
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Algebra.Com's Answer #700682 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
The identity I'll use is\r
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\n" ); document.write( "\n" ); document.write( "sin(x+y) = sin(x)*cos(y) + cos(x)*sin(y)\r
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\n" ); document.write( "\n" ); document.write( "This identity will be used to transform the right side of the original equation like so\r
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\n" ); document.write( "\n" ); document.write( "sin(x) + cos(x) = sqrt(2)*sin(x+pi/4)
\n" ); document.write( "sin(x) + cos(x) = sqrt(2) * [sin(x)*cos(pi/4)+cos(x)*sin(pi/4)]
\n" ); document.write( "sin(x) + cos(x) = sqrt(2) * [sin(x)*(sqrt(2)/2)+cos(x)*(sqrt(2)/2)]
\n" ); document.write( "sin(x) + cos(x) = sqrt(2)*(sqrt(2)/2) * [sin(x)+cos(x)]
\n" ); document.write( "sin(x) + cos(x) = ((sqrt(2)*sqrt(2))/2) * [sin(x)+cos(x)]
\n" ); document.write( "sin(x) + cos(x) = (sqrt(2*2)/2) * [sin(x)+cos(x)]
\n" ); document.write( "sin(x) + cos(x) = (sqrt(4)/2) * [sin(x)+cos(x)]
\n" ); document.write( "sin(x) + cos(x) = (2/2) * [sin(x)+cos(x)]
\n" ); document.write( "sin(x) + cos(x) = 1 * [sin(x)+cos(x)]
\n" ); document.write( "sin(x) + cos(x) = sin(x) + cos(x)\r
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\n" ); document.write( "\n" ); document.write( "Note how the left side is kept the same. I only changed the right side. The last step confirms we have a true identity because we have the same expression on both sides. \n" ); document.write( "
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