Question

use basic identities to simplify: cosx-cosxsin^2x
and cotxsecxsinx

Answer 1

cosx-cosxsin²x
Factor cosx out.
cosx(1-sin²x) = cosx(cos²x) = cos³x

Answer 2

cotxsecxsinx

Knowing that \(\cot x = \dfrac{\cos x}{\sin x}\) and \(\sec x = \dfrac{1}{\cos x }\)

cotxsecxsinx = 1

Answer 3

thank you! what about proving this identity:
(cscx-1)/(cscx+1) = (cot^2x)/(csc^2x+2cscx+1)

Answer 4

Factor csc²x+2cscx+1

Then multiply both sides by (cscx + 1)²