삼각함수 구증: cos^2(a)-cos(2a)*cos(4a)=sin^2(3a) 구증: cos^2(a)-cos(2a)*cos(4a)=sin^2(3a)

삼각함수 구증: cos^2(a)-cos(2a)*cos(4a)=sin^2(3a) 구증: cos^2(a)-cos(2a)*cos(4a)=sin^2(3a)

왜냐하면
cos²a-cos2acos4a-sin²3a
=(1+cos2a)/2-cos2acos4a-(1-cos6a)/2
=cos2a/2-cos2acos4a+cos6a/2
=cos2a/2-cos2acos4a+(cos2acos4a-sin2asin4a)/2
=cos2a/2-(cos2acos4a+sin2asin4a)
=cos2a/2-cos(2a-4a)/2
=cos2a/2-cos(2a)/2
=0
그래서
cos^2a-cos2acos4a=sin^2 3a