Simplify: csc^2x-1/csc^2+1

Question

It had to be equal to cscx-sinx/cscx+sinx

Answer 1

 

[1/sin^2 - 1 ] / [ 1/sin^2 + 1 ] =    <-----        cscx = 1/sin x

 

[1 - sin^2 ]/sin^2   divided by [ 1 + sin^2]/sin^2  <---- resolves the complex, nested fractions

 

(1 - sin^2)/(1 + sin^2) =    <--- denominators cancel out

 

csc x - sin x / csc x + sin x   <--- divides top and bottom by sin x

 

 

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I figured it out by doing.....

 

cscx - sinx / csc x + sin x

 

1 - sin^2 / 1 + sin^2

 

and then saw it was the same as what I had up above,

but going backwards