How do you simplify tanx/(1-tanx)+cosx/(sinx-cosx)?

1 Answer
sente
Oct 11, 2016

tan(x)/(1-tan(x))+cos(x)/(sin(x)-cos(x))=-1 for x !in {pi/2+pik, pi/4+pik}

Explanation:

For x !in {pi/2+pik, pi/4+pik}

tan(x)/(1-tan(x))+cos(x)/(sin(x)-cos(x))

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

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

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

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

=-1

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