Cho a là góc nhọn rút gọn biểu thức ;sin^6a + cos^6a + 3 sin^2 a – cos^2 a 03/07/2021 Bởi Athena Cho a là góc nhọn rút gọn biểu thức ;sin^6a + cos^6a + 3 sin^2 a – cos^2 a
`=sin^6a+cos^6a+3sin^2a-cos^2a` `= (sin^2a )^3+ (cos^3a )^2+3sin^2a-cos^2a` `= (sin^2a+cos^2a )^3-3sin^2a.cos^2a (sin^2a+cos^2a )+3sin^2a-cos^2a` `=1-3sin^2a.cos^2a+3sin^2a-cos^2a` `=3sin^2a-3sin^2a.cos^2a+1-cos^2a` `=3sin^2a (1-cos^2a )+ (1-cos^2a )` `= (3sin^2a+1 ) (1-cos^2a )` `= (3sin^2a+1 ) (sin^2a )=3sin^4a+sin^2a` Bình luận
`=sin^6a+cos^6a+3sin^2a-cos^2a`
`= (sin^2a )^3+ (cos^3a )^2+3sin^2a-cos^2a`
`= (sin^2a+cos^2a )^3-3sin^2a.cos^2a (sin^2a+cos^2a )+3sin^2a-cos^2a`
`=1-3sin^2a.cos^2a+3sin^2a-cos^2a`
`=3sin^2a-3sin^2a.cos^2a+1-cos^2a`
`=3sin^2a (1-cos^2a )+ (1-cos^2a )`
`= (3sin^2a+1 ) (1-cos^2a )`
`= (3sin^2a+1 ) (sin^2a )=3sin^4a+sin^2a`