Question

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

Answer 1

@MrNood

Answer 2

soz - can't help right now

Answer 3

thx anyways

Answer 4

the answer is simply an integer (I graphed it) but haven't got time ot prove it analytically

Answer 5

not sin @ = x and cos @ = y

so then will get

(x-y)^2 +(x+y)^2 = x^2 -2xy +y^2 +x^2 -2xy +y^2 = 2x^2 +2y^2 = 2(x^2 +y^2)=
=2(sin^2 @ +cos^2 @) = 2*1 =2

(x-y)^2 = x^2 -2xy +2
(x+y)^2 = x^2 +2xy +y^2

hope this will help you sure easy

Answer 6

ok ?

Answer 7

i dont understand

Answer 8

why ? this is very easy or you dont know formula sin^2 x +cos^2 x =1 ?

Answer 9

sorry need being y^2

(x-y)^2 = x^2 -2xy +2

the last term is y^2

Answer 10

now im even more confused

Answer 11

Ok @Jessievb lets start from beginning. Ok ?

Answer 12

ok

Answer 13

We have to simplify \[\large{(\sin {\theta} - \cos \theta)^2 + (\sin \theta + \cos \theta)^2}\]

Answer 14

First lets expand the square terms.

We use this formula:

\[\large{(a+b)^2 = a^2 + 2ab + b^2}\]

Any doubt ?

Answer 15

no

Answer 16

We use the above formula to expand the term - \(\large{(\sin \theta + \cos \theta)^2}\)

Similarly we use the formula : \(\large{(a-b)^2 = a^2 - 2ab + b^2}\) to expand the term:\(\large{(\sin \theta - \cos \theta)^2}\)

Answer 17

Thus:

\[\large{(\sin \theta - \cos \theta)^2 = \sin^2 \theta - 2\times \sin \theta \times \cos \theta + \cos^2 \theta}\]

And :

\[\large{(\sin \theta + \cos \theta)^2 = \sin^2 \theta + 2\times \sin \theta \times \cos \theta + \cos^2 \theta}\]

Any doubt ?

Answer 18

not really

Answer 19

is the answer going to be a number?

Answer 20

@vishweshshrimali5

Answer 21

@quickstudent @WiredCardinal08 @phi @cwrw238

Answer 22

@Jessievb
You really do have ALL the information given above to solve this.

In the time it takes for someone else to answer you - oyu could try doing it your self

ignore the sin and cos for now

(a+b)^2 + (a-b)^2

simplifies to 2(a^2+b^2)

NOW put the sin and cos back in - and take it from there....

Answer 23

ive been trying for the past half hour!
so the answer is 2

Answer 24

??

Answer 25

Show how you get that answer...

Answer 26

sin and cos = 1 i think

Answer 27

??

Answer 28

doesnt sin and cos cancel each other out or something

Answer 29

that doesn't sound like much of a mathematical analysis!
Try again???

Answer 30

is the answer two? its my homework and my teacher grades hw. Ill ask her to explain it to me cause im confused