# c4

#1
cos^2x - sin^" x = cos2x
They're both equal to each other according to the book, can someone elaborate why please?
0
4 years ago
#2
That's just a basic theorem that you need to know.
It's just a weaker form of the compound angle formula for cos:
cos(x+y) = cos(x)cos(y) - sin(x)sin(y)
and you just make x=y to get your formula above.

There are many proofs for the compound angle formula.
Here's one that's nice and geometric:

1
4 years ago
#3
(Original post by Chelsea12345)
cos^2x - sin^" x = cos2x
They're both equal to each other according to the book, can someone elaborate why please?
If you use the formula book and look at trig identity cos (A+B) and if x is A and B .. it will make cos (2x)=cos(x)cos (x)-sin (x)sin (x)
Cos (2x)=cos^2x-sin^2x
1
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