Question #8de97

2 Answers
Dec 10, 2016

That is not an identity.

Explanation:

Recall that

cot^2x+1 = csc^2x.

So, we can write

(1-csc^2x)/csc^2x = (1-(cot^2x+1))/csc^2x

= cot^2x/csc^2x

Recall also that cotx = cosx/sinx and cscx = 1/sinx.

This allows us to continue

= (cos^2x/sin^2x)/(1/sin^2x)

= cos^2x/sin^2x * sin^2x/1

= cos^2x

Which is not identically cosx.

(cos^2x = cosx only when cosx = 1 or 0)

Dec 10, 2016

No. It is equal to sin^2x - 1.

Explanation:

If we have (1 - x)/x, we can write it as 1/x - x/x.

The same way, (1 - csc^2 x)/csc^2 can be written as 1/csc^2x - (csc^2x)/(csc^2x).

This is equal to sin^2x - 1.