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You can put this solution on YOUR website!
let x = theta.
\n" ); document.write( "this is not necessary, but easier to type.
\n" ); document.write( "problem becomes:
\n" ); document.write( "(sin(x) - csc(x) / cos(x)
\n" ); document.write( "csc(x) = 1/sin(x), therefore the expression becomes:
\n" ); document.write( "(sin(x) - 1/sin(x)) / cos(x)
\n" ); document.write( "multiply numerator and denominator by sin(x) to get:
\n" ); document.write( "(sin^2(x) - 1) / (sin(x)cos(x))
\n" ); document.write( "sin^2(x) - 1 = -(1 - sin^2(x) = -cos^2(x), therefore the expression becomes:
\n" ); document.write( "-cos^2(x) / (sin(x)cos(x))
\n" ); document.write( "divide numerator and denominator by cos(x) to get:
\n" ); document.write( "-cos(x) / sin(x)
\n" ); document.write( "since this is equivalent to -cot(x), then you have:
\n" ); document.write( "(sin(x) - csc(x) / cos(x) = -cot(x)
\n" ); document.write( "that's your solution, as far as i can see.
\n" ); document.write( "confirm by assigning any angle that pops into your head.
\n" ); document.write( "i'm working in degrees, so make sure your calculator is working in degrees if you want to try this yourself.
\n" ); document.write( "i chose 3 angles at random.
\n" ); document.write( "-cot(x) is confirmed to be equivalent to (sin(x) - csc(x)) / cos(x) for all 3 of them.
\n" ); document.write( "for example, if i chose 257936 degrees:
\n" ); document.write( "(sin(x) - csc(x) / cos(x) = 14.30066626
\n" ); document.write( "-cot(x) = 14.30066626
\n" ); document.write( "sine they're the same, the two expressions are equivalent.
\n" ); document.write( "note that csc(x) = 1/sin(x) and cot(x) = 1/tan(x).
\n" ); document.write( "if your calculator can't handle csc(x) or cot(x) directly, you will need to use those equivalents.
\n" ); document.write( " \n" ); document.write( "