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# Trigonometry

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1. Hi, I'm not sure how to do this question, so any help would be greatly appreciated!
Prove that (cosx + sinx)2 + (cosx - sinx)2 = 2
2. Expand each set of brackets out and use the identity .
3. (Original post by B_9710)
Expand each set of brackets out and use the identity .
what's with the 3 lines with the = sign? does it mean something significant?
4. (Original post by thefatone)
what's with the 3 lines with the = sign? does it mean something significant?
Identical to. Equal for all x.
5. (Original post by thefatone)
what's with the 3 lines with the = sign? does it mean something significant?
Always equal, no matter the value of x
6. (Original post by KaylaB)
Always equal, no matter the value of x
oh ok
7. (Original post by thefatone)
oh ok
.
8. (Original post by B_9710)
.
does the lines mean the magnitude of x?
9. (Original post by thefatone)
does the lines mean the magnitude of x?
Yes the absolute value. |-2|=2
10. (Original post by B_9710)
Yes the absolute value. |-2|=2
wait so you put the root of x² is exactly the same as the size of x? wat isn't that obvious??
11. (Original post by thefatone)
wait so you put the root of x² is exactly the same as the size of x? wat isn't that obvious??
People often make the mistake that .
But it doesn't. Try it with a negative value of x and you'll see why what I have put here cannot be true.
12. (Original post by B_9710)
People often make the mistake that .
But it doesn't. Try it with a negative value of x and you'll see why what I have put here cannot be true.
so does the formula ?
13. (Original post by thefatone)
so does the formula ?
No. There is no value that returns a negative value from the square root. You can't square root something and get a negative answer.
14. (Original post by B_9710)
No. There is no value that returns a negative value from the square root. You can't square root something and get a negative answer.
oops fixed it

but surely you square the number first? since that's inside the square root?
15. (Original post by thefatone)
oops fixed it

but surely you square the number first? since that's inside the square root?
What you have put above is incorrect. You cannot square root something and get a negative answer. Let's take -1 as an example.
.
16. (Original post by B_9710)
What you have put above is incorrect. You cannot square root something and get a negative answer. Let's take -1 as an example.
.
but doesn't my calculator tells me this is true....

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