Question #2f3e9

1 Answer
sente
May 23, 2016

Presumably this was intended as 1-cos(x)sin(x)cot(x) = sin^2(x), and will be answered as such.

Using the definition of the cotangent function cot(x) = cos(x)/sin(x), along with the identity

sin^2(x)+cos^2(x) = 1 => sin^2(x) = 1-cos^2(x)

we have, for sin(x)!=0,

1-cos(x)sin(x)cot(x) = 1-cos(x)sin(x)cos(x)/sin(x)

=1-(sin(x)cos(x)cos(x))/sin(x)

=1-cos^2(x)

=sin^2(x)

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