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

Question

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#?

1727 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-02T02:54:11

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

#(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#