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kkristazz
@kkristazz
July 2022
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100 баллов . Доказать тождество. алгебра 9 класс
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армения20171
Verified answer
Cos^8(a)-sin^8(a)=0,25•cis2a(3+cos4a)
(cos⁴a)²-(sin⁴)²=(cos⁴a-sin⁴a)(cos⁴a+sin⁴a)
=(cos²a+sin²a)(cos²a-sin²a)(cos⁴a+sin⁴a)
=cos2a•((cos²a)²+2cos²asin²a+(sin²a)²-
2sin²a•cos²a)=cos2a•((sin²a+cos²a)²-2sin²a•
cos²a)=cos2a•(1-2sin²acos²a)=
cos2a•(1-1/2sin²2a)=cos2a•(2-sin²2a)•1/2=
1/2*cos2a*(2-(1-cos4a)/2)=
1/4*cos2a*(4-1+cos4a)=
0,25cos2a(3+cos4a)
1 votes
Thanks 3
kkristazz
спаасибо огромное
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Answers & Comments
Verified answer
Cos^8(a)-sin^8(a)=0,25•cis2a(3+cos4a)(cos⁴a)²-(sin⁴)²=(cos⁴a-sin⁴a)(cos⁴a+sin⁴a)
=(cos²a+sin²a)(cos²a-sin²a)(cos⁴a+sin⁴a)
=cos2a•((cos²a)²+2cos²asin²a+(sin²a)²-
2sin²a•cos²a)=cos2a•((sin²a+cos²a)²-2sin²a•
cos²a)=cos2a•(1-2sin²acos²a)=
cos2a•(1-1/2sin²2a)=cos2a•(2-sin²2a)•1/2=
1/2*cos2a*(2-(1-cos4a)/2)=
1/4*cos2a*(4-1+cos4a)=
0,25cos2a(3+cos4a)