Question

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

Answer 1

Here are the answers:

−sin2 Θ

−cos2 Θ

0

2

Answer 2

@Venny

Answer 3

Let us look at the algebraic identities:
(a+b)^2 = a^2 + 2ab + b^2
(a-b)^2 = a^2 - 2ab + b^2
add
(a+b)^2 + (a-b)^2 = 2a^2 + 2b^2 = 2(a^2 + b^2)

Therefore, (sin Θ − cos Θ)^2 + (sin Θ + cos Θ)^2 = ?

Answer 4

Idk

Answer 5

Okay, why don;t you just go ahead and expand (sin Θ − cos Θ)^2 first

Answer 6

\[\sin \theta^2-\cos \theta^2\]

Answer 7

No. The algebraic identity to use here is: (a-b)^2 = a^2 - 2ab + b^2

Answer 8

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

Answer 9

(sin Θ − cos Θ)2 + (sin Θ + cos Θ)2 simplifies to 4sin(Θ)
I assume that you meant ^2 as opposed to 2 in the original question, therefore your answer is 2. If you need me to explain more I can later, I'm on my mobile at the moment and typing is horrendously difficult.

Answer 10

\((\sin \theta - \cos \theta)^2 = \sin^2 \theta-2(\sin \theta)(\cos \theta)+\cos^2 \theta\)
\((\sin \theta + \cos \theta)^2 = \sin^2 \theta+2(\sin \theta)(\cos \theta)+\cos^2 \theta\)
Add:
\((\sin \theta - \cos \theta)^2 + (\sin \theta + \cos \theta)^2 = 2\sin^2 \theta +2\cos^2 \theta = 2(\sin^2 \theta +\cos^2 \theta ) = 2\)

Answer 11

THANKYOU SOO MUCHH IT WAS CORRECt!! (Just took the test XD)