document.write( "Question 738948: use the half angle identities to find all solutions in the interval [0,2pi) sin^2x=cos^2(x/2) \n" ); document.write( "

Algebra.Com's Answer #450965 by lwsshak3(11628) $\"\"$ $\"About$

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use the half angle identities to find all solutions in the interval [0,2pi) sin^2x=cos^2(x/2)
\n" ); document.write( "***
\n" ); document.write( " $\"sin%5E2%28x%29=cos%5E2%28x%2F2%29\"$
\n" ); document.write( " $\"cos%28x%2F2%29=sqrt%28%281%2Bcos%28x%29%29%2F2%29\"$
\n" ); document.write( " $\"cos%5E2%28x%2F2%29=%281%2Bcos%28x%29%29%2F2\"$
\n" ); document.write( " $\"sin%5E2%28x%29=%281%2Bcos%28x%29%29%2F2\"$
\n" ); document.write( " $\"2sin%5E2%28x%29=%281%2Bcos%28x%29%29\"$
\n" ); document.write( " $\"2%281-cos%5E2%28x%29%29=%281%2Bcos%28x%29%29\"$
\n" ); document.write( " $\"%282-2cos%5E2%28x%29%29=%281%2Bcos%28x%29%29\"$
\n" ); document.write( " $\"%282cos%5E2%28x%29%29%2Bcos%28x%29-1=0%29\"$
\n" ); document.write( " $\"%282cos%28x%29-1%29%28cos%28x%29%2B1%29=0\"$
\n" ); document.write( "..
\n" ); document.write( "2cos(x)-1=0
\n" ); document.write( "cos(x)=1/2
\n" ); document.write( "x=π/3, 5π/3
\n" ); document.write( "..
\n" ); document.write( "cos(x)+1=0
\n" ); document.write( "cos(x)=-1
\n" ); document.write( "x=π \n" ); document.write( "

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