Question

How do you prove? Csc^2 X - 1/ 1 + csc^2 x= cot^2 x

Answer 1

The equation is not valid.

Explanation:

.

`(csc^2x-1)/(1+csc^2x)=(1/sin^2x-1)/(1+1/sin^2x)=((1-sin^2x)/sin^2x)/((sin^2x+1)/sin^2x)=(1-sin^2x)/(sin^2x+1)=cos^2x/(sin^2x+1)`

Since `cot^2x=cos^2x/sin^2x`, the equation is not valid.