document.write( "Question 731409: Csc(3x-15)=sec(10+2x) \n" ); document.write( "

Algebra.Com's Answer #447112 by lwsshak3(11628) $\"\"$ $\"About$

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Csc(3x-15)=sec(10+2x)
\n" ); document.write( "1/sin(3x-15)=1/cos(2x+10)
\n" ); document.write( "[cos(2x+10)/sin(3x-15)]=1
\n" ); document.write( "For this equation to be true, the angles for both sin and cos must be=π/4
\n" ); document.write( "..
\n" ); document.write( "2x+10=π/4
\n" ); document.write( "2x=π/4-10
\n" ); document.write( "x=(π/4-10)/2
\n" ); document.write( "x≈-4.6073
\n" ); document.write( "..
\n" ); document.write( "3x-15=π/4
\n" ); document.write( "x=π/4+15)/3
\n" ); document.write( "x≈5.2618
\n" ); document.write( "Check:with calculator
\n" ); document.write( "cos(2x+10)=cos(2*-4.6073+10)≈0.7071
\n" ); document.write( "sin(3x-15)=sin(3*5.2618-15)=0.7071
\n" ); document.write( "[cos(2x+10)/sin(3x-15)]=0.7071/0.7071=1 \n" ); document.write( "

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