Question

Упростите выражение: 1/ 1 + sin a (sin a/ 2 + cos a/ 2)^2

Answer 1

$frac {1}{1+sina}(sinfrac{a}{2}+cosfrac{a}{2}))^{2}= frac{1}{1+sina}(sin^{2} frac{a}{2}+2sinfrac{a}{2}cosfrac{a}{2}+ cos^{2}frac{a}{2})= frac{1}{1+sina}(1+sin(2*frac{a}{2})= frac{1}{1+sina}(1+sin(2*frac{a}{2})=frac{1}{1+sina}(1+sin a)=1.$

 

ответ: 1