Question

Arătati ca sinx(3sinx-cosx)+cosx(sinx+3cosx)=3, pentru orice numar real x.​

Answer 1

sin x(3sin x-cos x)+cos x(sin x+3cos x)=

=3sin²x-sin x×cos x+cos x×sin x+3cos²x=

=3sin²x+3cos²x=

=3(sin²x+cos²x)=

=3×1=3