document.write( "Question 847607: cot(x/2)=1/3 find csc(x/2) \n" ); document.write( "

Algebra.Com's Answer #510614 by lwsshak3(11628) $\"\"$ $\"About$

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for[0,π/2]
\n" ); document.write( "cot(x/2)=1/3 find csc(x/2)
\n" ); document.write( "tan(x/2)=3
\n" ); document.write( "Identity: tan(x/2)=sinx/(1+cosx)
\n" ); document.write( "sinx/(1+cosx)=3
\n" ); document.write( "sinx=3+3cosx
\n" ); document.write( "3cosx=sinx-3
\n" ); document.write( "3√(1-sin^2x)=sinx-3
\n" ); document.write( "square both sides:
\n" ); document.write( "9(1-sin^2x)=sin^2x-6sinx+9
\n" ); document.write( "9-9sin^2x=sin^2x-6sinx+9
\n" ); document.write( "10sin^2x-6sinx=0
\n" ); document.write( "5sin^2x-3sinx=0
\n" ); document.write( "sinx(5sinx-3)=0
\n" ); document.write( "sinx=0 (reject,sinx>0)
\n" ); document.write( "or
\n" ); document.write( "sinx=3/5(in Q2)
\n" ); document.write( "cosx=-4/5(in Q2)
\n" ); document.write( "Identity:sin(x/2)=√((1-cosx)/2)=√((1-(-4/5))/2)=√((9/5)/2)=√(9/10)=3/√10
\n" ); document.write( "csc(x/2)=1/sin(x/2)=√10/3
\n" ); document.write( "calculator check:
\n" ); document.write( "tan(x/2)=3
\n" ); document.write( "x/2≈71.56˚
\n" ); document.write( "sin(x/2)=3/√10
\n" ); document.write( "x/2≈71.56˚ \n" ); document.write( "

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