Question

  Решить уравнение:        (cosx + sinx)^2 = cos2x

Answer 1

$(cosx+sinx)^2=cos2x \ cos^2x+sin^2x+2sinx*cosx=cos^2x-sin^2x \ 2sin^2x+2sinx*cosx=0 \ 2sinx(sinx+cosx)=0 \ 2sinx=0 \ sinx=0 \ x_1=(-1)^k*arcsin0+ pi k \ x_1= pi k \ sinx+cosx=0|:cosx \ frac{sinx}{cosx} +1=0 \ tgx+1=0 \ tgx=-1 \ x_2=arctg(-1)+ pi n \ x_2=- frac{ pi }{4} + pi n$