## itsonlycdeee 2 years ago 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 =

1. cwrw238

sin^2θ/cosθ = (1 - cos^2θ)/cosθ = 1 / cosθ - cos θ = secθ - cos θ

2. hartnn

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 :)

3. itsonlycdeee

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

4. hartnn

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

5. itsonlycdeee

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

6. hartnn

you're most welcome ^_^

7. cwrw238

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

8. itsonlycdeee

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