Question 861255
prove that these are equal..... 
cot^2x-1/1+cot^2x=1-2sin^2x
{{{(cot^2(x)-1)/(cot^2(x)+1)=1-2sin^2(x))}}}
start with left side:
{{{(cot^2(x)-1)/(cot^2(x)+1)=(cos^2(x)/sin^2(x)-1)/(cos^2(x)/sin^2(x)+1)}}}
...
{{{(cos^2(x)-sin^2(x))/(cos^2(x)+sin^2(x))=cos^2(x)-sin^2(x)}}}
...
{{{cos^2(x)-sin^2(x)=1-sin^2(x)-sin^2(x)=1-2sin^2(x)}}}
...
verified: left side=right side