document.write( "Question 920175: prove csc(5pi/2 -x)=secx \n" ); document.write( "

Algebra.Com's Answer #558273 by lwsshak3(11628) $\"\"$ $\"About$

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prove csc(5pi/2 -x)=secx
\n" ); document.write( "csc(5π/2-x)=secx
\n" ); document.write( "start with left side:
\n" ); document.write( "csc(5π/2-x)=1/sin(5π/2-x)
\n" ); document.write( "using sin addition formula: sin(x-y)=sinxcosy-cosxsiny
\n" ); document.write( "sin(5π/2-x)=(sin(5π/2)*cosx-cos(5π/2)*sin(x)
\n" ); document.write( "=(1*cosx-0*sinx)=cosx
\n" ); document.write( "csc(5π/2-x)=1/sin(5π/2-x)=1/cosx=secx
\n" ); document.write( "verified: left side=right side
\n" ); document.write( "note: 5π/2=reference angle of π/2 \n" ); document.write( "

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