rozwiąż równanie trygonometryczne (sinx[latex](sinx + cosx)^{2} = cos2x[/latex] 

(sinx+cosx)² = cos2x sin²x+2sinxcosx+cos²x = cos2x 1+2sinxcosx = cos2x 1+2sinxcosx = cos²x-sin²x 1+2sinxcosx = 1-sin²x-sin²x 2sinxcosx = -2sn²x 2sinxcosx+2sin²x = 0 2sinx(cosx+sinx) = 0 sinx = 0    => x = kπ lub cosx+sinx = 0 sinx = -cosx  /:cosx sinx/cosx = -cox/cosx tgx = -1    => x = -π/4 +kπ Odp. x = kπ  lub  x = 3π/4 + kπ,  k∈C.