How do you verify the identity #sec^2xcotx-cotx=tanx#?

Question

15479 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-17T20:18:24

see below

Left Hand Side:

#sec^2x cot x - cot x=cotx(sec^2x-1)#

Use identity: #1+tan^2x=sec^2x#

#=cotxtan^2x#

#=cosx/sinx * sin^2x/cos^2x#

#=cancelcosx/cancelsinx * sin^cancel2x/cos^cancel2x#

#=sinx/cosx#

#=tanx#

#:.=# Right Hand Side