Question

sin 25x/2+cos 25x/2=1
Помогите решить ​

Answer 1

$sinfrac{25x}{2}+cosfrac{25x}{2}=1; |:sqrt2\\frac{1}{sqrt2}cdot sinfrac{25x}{2}+frac{1}{sqrt2}cdot cosfrac{25x}{2}=frac{1}{sqrt2}\\cosfrac{pi}{4}cdot  sinfrac{25x}{2}+sinfrac{pi}{4}cdot cosfrac{25x}{2}=frac{sqrt2}{2}\\sin(frac{25x}{2}+frac{pi}{4})=frac{sqrt2}{2}\\frac{25x}{2}+frac{pi}{4}=(-1)^{n}cdot frac{pi}{4}+pi n,; nin Z\\frac{25x}{2}=-frac{pi}{4}+(-1)^{n}cdot frac{pi}{4}+pi n; ,; nin Z\\x=-frac{pi }{50}+(-1)^{n}cdot frac{pi}{50}+frac{2pi n}{25}; ,; nin Z$