Question

Please help kinda in a hurry
Simplify: (sin Θ − cos Θ) − (sin Θ + cos Θ)^2

−sin^2 Θ
−cos^2 Θ
0
−2sin(Θ)cos(Θ) − cos(Θ) + sin(Θ) − 1

Answer 1

Hint

(a + b)^2 = a^2 + 2ab + b^2

Use that to expand (sin Θ + cos Θ)^2

and then simply add and subtract like terms, if there are any :)

Answer 2

first of all, please expand (sin theta + cos theta)^2.

Note that exponentiation (such as squaring) has to be done before addition/subtraction.

Answer 3

so a represents sin and b represents cos right?

Answer 4

(sin+cos)^2=sin^2+2sincos+cos^2

Answer 5

correct :)

Now, do you know the identity sin^2Θ + cos^2Θ = 1

Use that to simplify
sin^2Θ+2sinΘcosΘ+cos^2Θ

Answer 6

Not really familiar with it to much kinda new to this stuff
1+sin (2Θ)?

Answer 7

Leave 2sinΘcosΘ as is.

Now simplify
(sinΘ - cosΘ) - (2sinΘcosΘ + 1)

Answer 8

Since none of the answer choices have sin(2Θ)

Answer 9

Can I combine the sin and cos in the first parenthesis with the second ones?

Answer 10

no, they aren't like terms

Answer 11

It's like how you can't simplify x + y + 2xy any more further

Answer 12

-1-cos(Θ)-sin(2Θ)+sin (Θ)?

Answer 13

I put it into a calculator and thats what I got

Answer 14

yes, but instead replace sin(2Θ) with 2sinΘcosΘ

Answer 15

-1-cos(Θ)-sin(2sinΘcosΘ)?

Answer 16

nvm

Answer 17

-1-cos(Θ)-2sinΘcosΘ+sin (Θ)

Answer 18

Correct

That would be D

Answer 19

Oh so you just re-arrange the like terms like they were like 2x time 2y is also 2y times 2x?

Answer 20

Awesome it was correct thank you so much!

Answer 21

Anytime! :)