Question

Prove the following trigonometric identity and show your work: (in other words, show that the identities on the left equal the one on the right). Please show all of your work.

cos t(sect- cos t=sin^2 t

Answer 1

cos t*sec t-cost *cost=sin ² t
sec t =1/(cos t)
cost*1/(cos t) -cos² t=sin² t
1-cos² t= sin² t
sin² t =sin² t true, so
cos t(sect- cos t)= sin²t true

Answer 2

cos t(sect- cos t)

sec t = 1/cos t so

= cos t( 1/cos t - cos t)
= cos t / cos t - cos²t (distribute)
= 1 - cos²t
since sin²t + cos²t = 1, we have sin²t = 1 - cos²t
so
= sin² t
=right-hand side