Prove the following trigonometric identity and show your work: (in other words, show that the identities on the left equal the o

Question

777dan777 [17]

4 years ago

5

Prove the following trigonometric identity and show your work: (in other words, show that the identities on the left equal the o

ne on the right). Please show all of your work.
cos t(sect- cos t=sin^2 t

Mathematics

2 answers:

loris [4] · Answer 1 · 2022-01-11T20:14:05+03:00

loris [4]4 years ago

6 0

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
<span>cos t(sect- cos t)= sin²t true</span>

Aleks04 [339] · Answer 2 · 2022-01-11T17:52:58+03:00

Aleks04 [339]4 years ago

5 0

<span>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

</span>