Доказать 3(sin^4a+cos^4a)-2(sin^6a+cos^a)=1 - вопрос №3734712344261 от artemchik25 17.06.2022 20:16

Question

Алгебра: Доказать 3(sin^4a+cos^4a)-2(sin^6a+cos^a)=1

artemchik25 · Answer

3(sin^4a+cos^4a)-2(sin^6a + cos^6a) =  3(sin^4a+cos^4a)-2(sin^2a+cos^2a)(sin^4a-sin^2a cos^2a+ cos^4a) =  3sin^4a + 3cos^4a- 2sin^4a+2sin^2a cos^2a – 2cos^4a  = sin^4a + 2sin^2a cos^2a+cos^4a = (sin^2a+cos^2a)^2 = 1...