Question

Упростите a) sina/2sin^2a/2 б) cos2a+sin^2a

Answer 1

$sf a)~ dfrac{sin alpha}{2sin^2frac{alpha}{2}}=dfrac{2sinfrac{alpha}{2}cosfrac{alpha}{2}}{2sin^2frac{alpha}{2}}=dfrac{cosfrac{alpha}{2}}{sinfrac{alpha}{2}}={rm ctg}, frac{alpha}{2}\ \ \ b)~ cos2alpha+sin^2alpha=cos^2alpha-sin^2alpha+sin^2alpha=cos^2alpha$