## anonymous one year ago Simplify: (sin Θ − cos Θ)2 + (sin Θ + cos Θ)2

1. anonymous

A. -sin^2Θ B. -cos^2Θ c. 2 d. 0

2. anonymous

3. kropot72

The first step is to expand the brackets. Expanding the first bracket we get $\large (\sin\theta-\cos\theta)^{2}=\cos^{2}\theta-2\sin\theta \cos\theta+\cos^{2}\theta$ What do you get when you expand the second bracket?

4. anonymous

hm not sure

5. anonymous

6. kropot72

The expansion of the second bracket is $\large \sin^{2}\theta+\sin\theta \cos\theta+\cos^{2}\theta$ Now you need to collect like terms in the sum of the two expansions and simplify.

7. anonymous

okay i understand so would the answer be A?

8. kropot72

Please don't guess the answer. The sum of the two expansions is $\large 2\sin^{2}\theta+2\cos^{2}\theta$ Now you need to simplify.

9. anonymous

so how would i simplify this??

10. kropot72

Well 2 is a common factor. So we get $\large 2(\sin^{2}\theta+\cos^{2}\theta)$ If you know your trig identities this can be easily simplified.

11. kropot72

What is the value of $\large \sin^{2}\theta+\cos^{2}\theta=?$

12. anonymous

im not sure im terrible at this

13. anonymous

would it equal 0 maybe?

14. kropot72

Not really. $\large \sin^{2}\theta+\cos^{2}\theta=1$

15. anonymous

so then you woiuld do 1 multiplyed by 2 and the answer would be 2?

16. kropot72

Correct!

17. anonymous

thank you so much

18. kropot72

You're welcome :)