Question

(sin Θ − cos Θ)2 − (sin Θ + cos Θ)2

Answer 1

−4sin(Θ)cos(Θ)
2
sin2 Θ
cos2 Θ

Answer 2

distribute, then combine terms

note : sin^2 + cos^2 = 1

Answer 3

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

Answer 4

\[a ^{2} - b ^{2} = (a-b)(a+b)\]

Answer 5

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

Answer 6

can you do it @gabbimanges17 ?

Answer 7

@UnkleRhaukus is the answer sin^2?

Answer 8

nope.

what do you get for (a-b)?

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

Answer 9

@UnkleRhaukus im not sure

Answer 10

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

Answer 11

looks like they cancel each other out

Answer 12

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

Answer 13

@UnkleRhaukus can you specify?

Answer 14

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

Answer 15

\[=\Big(\sin\theta +\sin\theta + \cos\theta − \cos\theta\Big)\Big(\sin\theta -\sin\theta - \cos\theta− \cos\theta\Big)\\
=\]

Answer 16

0

Answer 17

work it out properly

Answer 18

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

Answer 19

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

Answer 20

2?

Answer 21

you have me in a twist

Answer 22

simplify!

Answer 23

−4sin(Θ)cos(Θ)

Answer 24

are you sure?

Answer 25

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

Answer 26

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 ...

Answer 27

−4sin(Θ)cos(Θ)

Answer 28

good.

Answer 29

thank you!