## anonymous one year ago Simplify secθ + secθtan^2θ. A.) 1 B.) cosθ C.) secθ D.) sec^3θ

1. Nnesha

factor!

2. anonymous

3. Nnesha

sec theta = x tan theta = y so you can write it as $\huge\rm (x+xy^2)$ so what is common in these both terms ?

4. anonymous

x

5. Nnesha

yes right so take it out$\huge\rm x(1+y^2)$ now you can replace x and y by sec an tan $\huge\rm sec \theta (1+ \tan^2)$ 1+tan^2 = what ? ^^^^identity

6. anonymous

i still dont understand whatsoever.

7. Nnesha

it's same like simple algebra first we have to find GCF(greatest common factor) $\huge\rm sec \theta + \sec \theta \tan^2$ sec is common so take it out and divide both terms by common factor write your answer in the parentheses|dw:1434120062504:dw| $\sec \theta (1+ tan^2 \theta )$

8. anonymous

right now i feel like i must be missing something... because i dont understand what i am susposed to be understanding...

9. Nnesha

alright did you take notes ?

10. Nnesha

tag other users maybe they can explain better than me :-) :-) good luck!!! :-)

11. anonymous

kk

12. anonymous

@aloud @mathmath333 @mathmate

13. mathmate

As @Nnesha said, factor: secθ + secθtan^2θ what do you get?

14. anonymous

how do i factor?

15. mathmate

For example, factoring xy+xz = x(y+z)

16. mathmate

You take out the common factor from each term. It's like the inverse of distribution.

17. anonymous

right now, i guess my mind is still waking up. but i think i am starting to understand factoring...

18. mathmate

Well, hints I give would be: 1. factor out sec$$\theta$$ see https://www.mathsisfun.com/algebra/factoring.html for help 2. apply one of the pythagorean trig. identities. see http://www.sosmath.com/trig/Trig5/trig5/trig5.html for help.

19. anonymous

i give up.

20. Nnesha

Practice does not make perfect. Only $$\huge\rm \color{reD}{{Perfect~Practice}}$$ makes perfect. ~Vince Lombardi so practice!!