document.write( "Question 444897: How to find the exact value of the angle 67.5 using half-angle identities? It says for sin, cos, and tan... Thanks! \n" ); document.write( "
Algebra.Com's Answer #306783 by lwsshak3(11628)\"\" \"About 
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How to find the exact value of the angle 67.5 using half-angle identities? It says for sin, cos, and tan... Thanks!
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\n" ); document.write( "Half-Angle formulas
\n" ); document.write( "sin s/2=+-sqrt((1-cos s)/2), (note:+ or - answer depends on value of sin s/2 not sin s.)
\n" ); document.write( "cos s/2=+-sqrt((1+cos s)/2), (note:+ or - answer depends on value of cos s/2 not cos s.)
\n" ); document.write( "tan s/2=sin s/(1+cos s)
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\n" ); document.write( "sin 67.5=sin 135/2=sqrt((1-cos 135)/2)
\n" ); document.write( "=sqrt((1+√2/2)/2)=sqrt((2+√2)/4)
\n" ); document.write( "=sqrt(2+√2)/2
\n" ); document.write( "..
\n" ); document.write( "cos 67.5=cos 135/2=sqrt((1+cos 135)/2
\n" ); document.write( "=sqrt((1+(-√2/2))/2)=sqrt((1-√2/2))/2)
\n" ); document.write( "=sqrt((2-√2)/4)
\n" ); document.write( "=sqrt(2-√2)/2
\n" ); document.write( "..
\n" ); document.write( "tan 67.5=tan 135/2=sin 135/(1+cos 135)
\n" ); document.write( "=(√2/2)/1+(-√2/2)
\n" ); document.write( "=√2/2)/1-(√2/2))
\n" ); document.write( "=√2/(2-√2)\r
\n" ); document.write( "\n" ); document.write( "Note: ( + answers selected for sin & cos because 67.5º is in quadrant I where sin & cos are positive) \n" ); document.write( "
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