Question

Simplify: (sin Θ − cos Θ)2 + (sin Θ + cos Θ)2

Answer 1

A. -sin^2Θ
B. -cos^2Θ
c. 2
d. 0

Answer 2

please please help

Answer 3

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?

Answer 4

hm not sure

Answer 5

please help me out real quick

Answer 6

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.

Answer 7

okay i understand so would the answer be A?

Answer 8

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.

Answer 9

so how would i simplify this??

Answer 10

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.

Answer 11

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

Answer 12

im not sure im terrible at this

Answer 13

would it equal 0 maybe?

Answer 14

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

Answer 15

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

Answer 16

Correct!

Answer 17

thank you so much

Answer 18

You're welcome :)