Question

Simplify: (sin Θ − cos Θ)^2 + (sin Θ + cos Θ)^2
I'm pretty sure it's two?

Answer 1

yes it is two can you show how though?

Answer 2

(a-b)^2 + (a + b)^2
(a-b+ a + b)^2 - 2 (a-b)(a + b)
(2a)^2 - 2 ( a^2 - b^2)
2a^2 + 2b^2
2(a^2 + b^2)
a^2 + b^2 = 1
so 2(a^2 + b^2) = 2

Answer 3

I squared the whole thing, then subtracted cos from cos and added sin to sin

Answer 4

a = sin theta and b = cos theta

Answer 5

pardon me, I took the square root of the whole thing.

Answer 6

your wording is vague, but you got the right answer
the correct wording is:
expand the squares, collect the terms and add up
sin^2+con^2=1
-2cossin cancels with 2cossin

Answer 7

i don't see anywhere to do square root? that would be wrong

Answer 8

Since both expression in the parenthesis are squared, it can be simplified by taking the square root

Answer 9

noo wrong!
you can't use square root just because they squared

Answer 10

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

Answer 11

recall that \[\sin^2 \theta +\cos^2 \theta =1\]

Answer 12

\[-2\sin \theta \cos \theta +2\sin \theta \cos \theta =0\]

Answer 13

do you see why it is 2 now?

Answer 14

taking the square is cannot be used here at all
you can't just take the square root because you see the square so careful
taking the square root is used in equations (ie cancels the square)

Answer 15

Where does the Pythagorean identity some in?

Answer 16

we are using square root in equations
because doing something in one side of the equation, we need to do the same thing the other side for the equation to hold otherwise it has no sense
maintain the balance of an equation

Answer 17

i'm not sure i understand your question, but i used the Pythagoras identity twice to give us 2
sin^2 theta +cos ^2 theta=1
see my reply above

Answer 18

Still don't get it but thanks anyways. :P

Answer 19

@onePieceFTW did you understand my response?