Question

Simplify: (sin Θ − cos Θ) − (sin Θ + cos Θ)2
can someone help?

Answer 1

hello??

Answer 2

-3

Answer 3

click best response

Answer 4

thats not an answer choice

Answer 5

the answer choices are:
−sin2 Θ
−cos2 Θ
0
−2sin(Θ)cos(Θ) − cos(Θ) + sin(Θ) − 1

Answer 6

well i dont know what to say because i got
Simplify the expression.
−3

Answer 7

what did you do to arrive to that conclusion?

Answer 8

(sin Θ − cos Θ) − (sin Θ + cos Θ)2

= sin Θ - cos Θ - ( sin^2 Θ + cos^2 Θ + 2 sin Θ cos Θ}

Now sin^2 Θ + cos^2 Θ = 1 and
2 sin Θ cos Θ = sin 2Θ
- can you continue?

Answer 9

no, i have no idea how to do this

Answer 10

Oh - no need to use that final identity

Answer 11

well replace sin^2 Θ + cos^2 Θ by 1 then just simplify

Answer 12

im still confused, what exactly am i simplifying

Answer 13

sin Θ - cos Θ - ( sin^2 Θ + cos^2 Θ + 2 sin Θ cos Θ}
= sin Θ - cos Θ - ( 1 + 2 sin Θ cos Θ}

Answer 14

now distribute the negative over the parentheses and you have the answer

Answer 15

-1-2sin(theta)cos(theta)?

Answer 16

what happened to the first 2 terms?

Answer 17

oh im sorry, let me retry

Answer 18

- the distribution you did is correct

Answer 19

wouldnt they just stay the same in front of what i did?

Answer 20

of course

Answer 21

okay, thats not an answer choice though

Answer 22

can it be further simplified?

Answer 23

no

Answer 24

im not sure whats wrong then
the answer choices are:
−sin2 Θ
−cos2 Θ
0
−2sin(Θ)cos(Θ) − cos(Θ) + sin(Θ) − 1

Answer 25

is it the last one and its just written differently?

Answer 26

Yes

they could have changed the fist part to - 2 sine theta but chose not to.

Answer 27

okay, thank you for all your help

Answer 28

* - sin 2 theta

Answer 29

yw