Question

Prove the identity.
sec θ − cos(−θ) = sin^2θ/cosθ

I'm trying to transform the left side to the right side & so far I got:

1/ cosθ - cos(-θ) =
1/cosθ - cosθ =

Answer 1

sin^2θ/cosθ

= (1 - cos^2θ)/cosθ

= 1 / cosθ - cos θ

= secθ - cos θ

Answer 2

if you want to continue from where you have left, try to make a common denominator
\(\dfrac{1}{\cos \theta}- \cos \theta \times \dfrac{\cos \theta}{\cos \theta}=\dfrac{1-\cos^2 \theta}{\cos \theta}\)
and lastly the use of \(\sin^2 x+\cos^2 x=1\) will lead you to right side :)

Answer 3

@hartnm okay, that's what I'm attempting right now.

Answer 4

good, did you get what i did ?
if yes, can you continue ?

Answer 5

Yes, it becomes sin^2θ/ cosθ. Thank you so much!

Answer 6

you're most welcome ^_^

Answer 7

with these problems its often easier to start with the more complicated side as i did here

Answer 8

@cwrw238 yeah, it'd take a few steps longer to go from the simpler side to the difficult one.