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

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1. anonymous

−4sin(Θ)cos(Θ) 2 sin2 Θ cos2 Θ

2. anonymous

distribute, then combine terms note : sin^2 + cos^2 = 1

3. UnkleRhaukus

use difference of squares, a^2 - b^2 = (a+b)(a-b)

$a ^{2} - b ^{2} = (a-b)(a+b)$

5. UnkleRhaukus

where a = sin Θ − cos Θ b = sin Θ + cos Θ

6. UnkleRhaukus

can you do it @gabbimanges17 ?

7. anonymous

8. UnkleRhaukus

nope. what do you get for (a-b)? and what do you get for (a+b)?

9. anonymous

@UnkleRhaukus im not sure

10. UnkleRhaukus

$(\sin\theta − \cos\theta)^2 − (\sin\theta + \cos\theta)^2$ $\Big((\sin\theta − \cos\theta)+(\sin\theta + \cos\theta)\Big)\Big((\sin\theta − \cos\theta)-(\sin\theta + \cos\theta)\Big)$

11. anonymous

looks like they cancel each other out

12. UnkleRhaukus

many of the terms cancel away, but not all of them

13. anonymous

@UnkleRhaukus can you specify?

14. UnkleRhaukus

$\color{teal}{(\sin\theta − \cos\theta)}^2 − \color{orange}{(\sin\theta + \cos\theta)}^2$ $=\Big(\color{teal}{(\sin\theta − \cos\theta)}+\color{orange}{(\sin\theta + \cos\theta)}\Big)\Big(\color{teal}{(\sin\theta − \cos\theta)}-\color{orange}{(\sin\theta + \cos\theta)}\Big)\\ =\Big(\sin\theta − \cos\theta+\sin\theta + \cos\theta\Big)\Big(\sin\theta − \cos\theta-\sin\theta - \cos\theta\Big)\\ =$

15. UnkleRhaukus

$=\Big(\sin\theta +\sin\theta + \cos\theta − \cos\theta\Big)\Big(\sin\theta -\sin\theta - \cos\theta− \cos\theta\Big)\\ =$

16. anonymous

0

17. UnkleRhaukus

work it out properly

18. anonymous

im not sure what youre asking.. it looks like the last two cos dont cancel out

19. UnkleRhaukus

$=\Big(\sin\theta +\sin\theta + \cos\theta − \cos\theta\Big)\Big(\sin\theta -\sin\theta - \cos\theta− \cos\theta\Big)\\ =\Big((1+1)\sin\theta + (1-1)\cos\theta\Big)\Big((1-1)\sin\theta +(-1-1)\cos\theta\Big)\\ =$

20. anonymous

2?

21. anonymous

you have me in a twist

22. UnkleRhaukus

simplify!

23. anonymous

−4sin(Θ)cos(Θ)

24. UnkleRhaukus

are you sure?

25. anonymous

im not sure about anything anymore, please can you explain in plain english

26. UnkleRhaukus

The expression given is a difference of squares, we used a formula we already knew for the difference of square to rearrange the expression. Then we simplified the terms in this new form, and we got ...

27. anonymous

−4sin(Θ)cos(Θ)

28. UnkleRhaukus

good.

29. anonymous

thank you!