Err... I would note that because the two expressions are identical (capitalization aside) that they, of course, express the same idea. However, since this is a rather absurd question to ask, I'm going to go out on a limb and assume that's not what you meant, and that you meant something along the lines of the following:
Is sin(x2) + cos(x2) = 1 the same thing as [sin(x)]^2 + [cos(x)]^2 = 1?
If the above is actually what you meant, then no, the two expressions do not mean the same thing. The former is only true for certain values of
x, whereas the latter is an identity, meaning it is true for all values of
x. If you want to prove it to yourself, one way you can do so is to use the product identities:
\(\displaystyle sin(x)sin(y)=\frac{cos\left(x-y\right)-cos\left(x+y\right)}{2}\) and \(\displaystyle cos(x)cos(y)=\frac{cos\left(x-y\right)+cos\left(x+y\right)}{2}\)
Here,
x and
y have the same value. What do you get if you make the appropriate substitution and simplify?
