Найти значение выражения √50cos^2 9π/8 - √50sin^2 9π/8

Question

Найти значение выражения

√50cos^2 9π/8 - √50sin^2 9π/8

Answer 1

√50cos² 9π/8 - √50sin² 9π/8=√50(cos²9π/8-sin²9π/8)=
 =√50cos(2*9π/8)=√50cos9π/4=√50cos(8π/4+π/4)=
=√50cos(2π+π/4)=√50cosπ/4=√50*√2/2=√100/2=10/2=5