Question

Решите уравнение: cos^2 (Пи/3 - 7х) = 1/2

Answer 1

Решение на фотографии

Answer 2

$cos^2( frac{pi}{3} -7x)= frac{1}{2} \cos^2( frac{pi}{3} -7x)- frac{1}{2} =0 \(cos( frac{pi}{3} -7x)- frac{sqrt{2}}{2} )(cos( frac{pi}{3} -7x)+ frac{sqrt{2}}{2} )=0 \cos(frac{pi}{3} -7x)- frac{sqrt{2}}{2}=0 \cos(frac{pi}{3} -7x)=frac{sqrt{2}}{2} \frac{pi}{3} -7x= frac{pi}{4} +2pi n \7x=frac{pi}{3}-frac{pi}{4}-2pi n \7x= frac{pi}{12} -2pi n \x_1= frac{pi}{84} - frac{2pi n}{7} , n in Z$
$frac{pi}{3} -7x=-frac{pi}{4} +2pi n \7x= frac{pi}{3} +frac{pi}{4} -2pi n \7x= frac{7pi}{12} -2pi n \x_2= frac{pi}{12} - frac{2pi n}{7}, n in Z \cos( frac{pi}{3} -7x)+ frac{sqrt{2}}{2} =0 \cos( frac{pi}{3} -7x)=-frac{sqrt{2}}{2} \ frac{pi}{3} -7x= frac{3pi}{4} +2pi n \7x=frac{pi}{3}-frac{3pi}{4}-2pi n \7x=- frac{5pi}{12} -2pi n \x_3=- frac{5pi}{84} - frac{2pi n}{7} , n in Z$
$frac{pi}{3} -7x=-frac{3pi}{4} +2pi n \7x=frac{pi}{3}+ frac{3pi}{4} -2pi n \7x= frac{13pi}{12} -2pi n \x_4= frac{13pi}{84} - frac{2pi n}{7}, n in Z$
Ответ: $x_1= frac{pi}{84} - frac{2pi n}{7} , n in Z; x_2= frac{pi}{12} - frac{2pi n}{7}, n in Z; x_3=- frac{5pi}{84} - frac{2pi n}{7} , n in Z\ x_4= frac{13pi}{84} - frac{2pi n}{7}, n in Z$