Question

若0度＜A＜30度,且sin^6(A)+cos^6(A)=7/12,那么1998cosA=

Answer 1

sin^6A+cos^6A=7/12

(sin²A+cos²A)(sin^4A-sin²Acos²A+cos^4A)=7/12

sin^4A+2sin²Acos²A+cos^4A-3sin²Acos²A=7/12

(sin²A+cos²A)²-3sin²Acos²A=7/12

1-3sin²Acos²A=7/12

sin²Acos²A=5/36

(2sinAcosA)²=5/9

sin²2A=5/9

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