How do I prove this identity? (cosxcotx-tanx)/cscx=cosx/secx-sinx/cotx

I've tried pretty much everything. I know it's true because I graphed them, and the lines are exactly the same. Is it valid to substitute a number for x?

1 Answer
May 2, 2018

The identity should be true for any number x that avoids division by zero.

Explanation:

(cosxcotx-tanx)/cscx

= {cos x (cos x/sin x) - sin x/cos x }/ (1/sin x )

= cos^2x - sin^2 x/cos x

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

=cosx/secx-sinx/cotx