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ПАшОк200
@ПАшОк200
July 2022
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a) 4-3sin^2(4x-5)=0
b) 2sin^2(2x)+7cos^2(2x)=3
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Dимасuk
Verified answer
А) 4 - 3sin²(4x - 5) = 0
4 = 3sin²(4x - 5)
sin²(4x - 5) = 4/3
Нет корней, т.к. sina ∈ [-1; 1].
б) 2sin²2x + 7cos²2x = 3
2sin²2x + 2cos²2x + 5cos²2x= 3
2 + 5cos²2x = 3
5cos²2x = 1
cos²2x = 1/5
cos2x = ±√5/5
2x = ±(arccos±√5/5) + 2πn, n ∈ Z
x = ±1/2(arccos±√5/5) + πn, n ∈ Z
(или x = 1/2(arccos(-√5/5)) + πn и 1/2(arccos √5/5) + πn, n ∈ Z).
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куда исчез синус ?
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Answers & Comments
Verified answer
А) 4 - 3sin²(4x - 5) = 04 = 3sin²(4x - 5)
sin²(4x - 5) = 4/3
Нет корней, т.к. sina ∈ [-1; 1].
б) 2sin²2x + 7cos²2x = 3
2sin²2x + 2cos²2x + 5cos²2x= 3
2 + 5cos²2x = 3
5cos²2x = 1
cos²2x = 1/5
cos2x = ±√5/5
2x = ±(arccos±√5/5) + 2πn, n ∈ Z
x = ±1/2(arccos±√5/5) + πn, n ∈ Z
(или x = 1/2(arccos(-√5/5)) + πn и 1/2(arccos √5/5) + πn, n ∈ Z).