Question

sinx+sin^2(x/2)=cos^2(x/2)

Решить уравнение

 

 

Answer 1

$sinx+sin^2(frac{x}{2})=cos^2(frac{x}{2})\ sinx=cos^2(frac{x}{2})-sin^2(frac{x}{2})\ (cos^2(frac{x}{2})-sin^2(frac{x}{2})=cos(2*frac{x}{2})=cosx)\ sin x=cosx\ tgx=1\x=frac{pi}{4}+pi n$