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You can put this solution on YOUR website!
prove:
\n" ); document.write( "(cscx-1)(1+cscx)=(cscx cosx)/(secx sinx)
\n" ); document.write( "I'm going to rewrite it this way:
\n" ); document.write( "(csc(x)-1)(1+csc(x)) = (csc(x)cos(x))/(sec(x)sin(x))
\n" ); document.write( "Multiply both sides by sin(x) and by sec(x):
\n" ); document.write( "sec(x)sin(x)(csc(x)-1)(1+csc(x)) = ^?cos(x)csc(x)
\n" ); document.write( "Write cosecant as 1/sine and secant as 1/cosine:
\n" ); document.write( "1/(cos(x))sin(x)(1/(sin(x))-1)(1+1/(sin(x))) = ^?1/(sin(x))cos(x)
\n" ); document.write( "((1/(sin(x)))-1)(1+(1/(sin(x))))(1/(cos(x)))sin(x) = ((1/(sin(x))-1)(1+1/(sin(x)))sin(x))/(cos(x)):
\n" ); document.write( "(sin(x)(1/(sin(x))-1)(1+1/(sin(x))))/(cos(x)) = ^?cos(x)(1/(sin(x)))
\n" ); document.write( "Put 1/(sin(x))-1 over the common denominator sin(x): 1/(sin(x))-1 = (1-sin(x))/(sin(x)):
\n" ); document.write( "((1-sin(x))/(sin(x))sin(x)(1+1/(sin(x))))/(cos(x)) = ^?(cos(x))/(sin(x))
\n" ); document.write( "Put 1+1/(sin(x)) over the common denominator sin(x): 1+1/(sin(x)) = (1+sin(x))/(sin(x)):
\n" ); document.write( "((1+sin(x))/(sin(x))sin(x)(1-sin(x)))/(sin(x)cos(x)) = ^?(cos(x))/(sin(x))
\n" ); document.write( "Cancel sin(x) from the numerator and denominator. ((1-sin(x))(1+sin(x))sin(x))/(sin(x)sin(x)cos(x)) = (sin(x)(-(sin(x)-1)(1+sin(x))))/(sin(x)sin(x)cos(x)) = -((sin(x)-1)(1+sin(x)))/(sin(x)cos(x)):
\n" ); document.write( "-((sin(x)-1)(1+sin(x)))/(cos(x)sin(x)) = ^?(cos(x))/(sin(x))
\n" ); document.write( "Cross multiply:
\n" ); document.write( "-sin(x)(sin(x)-1)(1+sin(x)) = ^?cos(x)^2 sin(x)
\n" ); document.write( "Divide both sides by sin(x):
\n" ); document.write( "-((sin(x)-1)(1+sin(x))) = ^?cos(x)^2
\n" ); document.write( "-(sin(x)-1)(1+sin(x)) = 1-sin(x)^2:
\n" ); document.write( "1-sin(x)^2 = ^?cos(x)^2
\n" ); document.write( "cos(x)^2 = 1-sin(x)^2:
\n" ); document.write( "1-sin(x)^2 = ^?1-sin(x)^2
\n" ); document.write( "Look at the left hand side and the right hand side. They are identical, so the identity has been verified. The equality is true \n" ); document.write( "