document.write( "Question 548058: find the exact solutions of the given equation in the interval [0 ,2TT] cos x/2- sin x = 0 \n" ); document.write( "

Algebra.Com's Answer #356740 by lwsshak3(11628) $\"\"$ $\"About$

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find the exact solutions of the given equation in the interval [0 ,2TT] cos x/2- sin x = 0
\n" ); document.write( "**
\n" ); document.write( "cos x/2- sin x = 0
\n" ); document.write( "using cos half-angle formula
\n" ); document.write( "cos(x/2)=√[(1+cosx)/2]
\n" ); document.write( "√[(1+cosx)/2]-sinx=0
\n" ); document.write( "√[(1+cosx)/2]=sinx
\n" ); document.write( "square both sids
\n" ); document.write( "(1+cosx)/2=sin^x=1-cos^2x
\n" ); document.write( "1+cosx=2-2cos^2x
\n" ); document.write( "2cos^2x+cosx-1=0
\n" ); document.write( "(2cosx-1)(cosx+1)=0
\n" ); document.write( "..
\n" ); document.write( "(2cosx-1)=0
\n" ); document.write( "2cosx=1
\n" ); document.write( "cosx=1/2
\n" ); document.write( "x=π/3 and 5π/3 (in quadrants I and IV where cos>0
\n" ); document.write( "or
\n" ); document.write( "cosx+1=0
\n" ); document.write( "cosx=-1
\n" ); document.write( "x=π
\n" ); document.write( "ans:
\n" ); document.write( "Exact solutions:
\n" ); document.write( "x=π/3, 5π/3 and π \n" ); document.write( "

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