How to evaluate $\cos(\frac{1}{2} \arcsin(\frac{1}{4}))$?

My thoughts

I tried to do double angle formula as in $\cos(2*\frac{1}{4}\arcsin(\frac{1}{4}))$

But that didn't work at all so then I tried to evaluate the arcsin inside of the expression but I had no success in finding the answer.


$\cos (x) = 2 \cos (x/2)^2-1,$ so $\cos(x/2) = \frac12 \sqrt{1+ \cos(x)}.$ Now, $\cos \arcsin (x) = \sqrt{1-x^2}.$ At this point you should be able to finish.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.