At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this and **thousands** of other questions.

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this and **thousands** of other questions

1. \[\cos (\cos^{-1} \frac{ 1 }{ 2 })=\frac{ 1 }{ 2 }\]

cos and cos-1 are inverses of each other. inverses cancel out. so yes 1 is correct

2.\[\cos (\cos^{-1} 2)=2 \]

same reasoning as 1.
inverses cancel out...

But I recall that my teacher told me that this is not the case in certain circumstances.

I'll ask him tomorrow.

cos^-1(2) is undefined, so cos(cos^-1(2)) is also undefined.

\[
\cos^{-1}:[-1,1]\mapsto [0,\pi]\\
\sin^{-1}:[-1,1]\mapsto [-\pi/2,\pi/2]
\]

No that's not true. See image attached.
You cannot calculate the inverse cosine of 2, which is what you would have to do here.
WolframAlpha can do it, because they use complex numbers, not real numbers.

you don't have to calculate arccos of 2. is my entire reasoning here.

See what I mean: http://www.wolframalpha.com/input/?i=arccos+2+
I rest my case.

woops yeah i was definitely wrong about that part
i blame it on st paddy day stupor

WA works with complex numbers as a default. Many people don't.