Simplify the expression:
ln(e^sinx^2)+ln(e^cosx^2)

Question

Simplify the expression:
ln(e^sinx^2)+ln(e^cosx^2)

perl · Answer

ln(e^u)=u

anonymous · Answer

Then what's left would be sinx^2+cosx^2?

anonymous · Answer

Yes :)

perl · Answer

and thats equal to 1, right?

anonymous · Answer

Who knows, really? :)
The problem with these things is that people see them differently...
Some people see
$$\large \cos x^2 + \sin x ^2$$Others see
$$\large (\cos x)^2+(\sin x )^2$$

Who's to say? ^_^

perl · Answer

obviously it means the latter

anonymous · Answer

Leave that to the asker.  Besides, I'm sure if it was the latter, it'd be written like
$$\large \cos^2x+\sin^2 x$$

anonymous · Answer

@peterpan, yeah, that's how it was written.

anonymous · Answer

Well, then it's settled.  Type cos^2 x next time, it will never be misinterpreted.
@perl no need to be so mean, I was just making sure.

anonymous · Answer

Alright, my bad

perl · Answer

peter, sorry

perl · Answer

peter, yes the way this person wrote it , it was ambiguous. because he doesnt know better :)

perl · Answer

but since it said 'simplify' , that would be simpler (1)

anonymous · Answer

Better safe than sorry.
Assuming is dangerous...

perl · Answer

it depends what youre doing

perl · Answer

better not to assume if you are running a 
nuclear reactor. its ok to assume when youre helping with homework

anonymous · Answer

It's ok, but is it better?

perl · Answer

better not assume when youre flying a plane,

perl · Answer

yes, because it can save time

anonymous · Answer

With a chance at error.  Besides, it did cause the asker to rectify the problem and/or settle things instead of leaving us wondering.