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Amsterdamus
@Amsterdamus
July 2022
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Упростите sin^4(x)-cos^4(x)-sin^2(x)+cos^2(x)
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ShirokovP
Verified answer
sin^4x - cos^4x - sin^2x + cos^2x =
= (sin^2x)^2 - (cos^2x)^2 - (sin^2x - cos^2x) =
= (sin^2x - cos^2x) * (sin^2x + cos^2x) -
(sin^2x - cos^2x) =
Вспомним, sin^2x + cos^2x = 1 ==>
=
(sin^2x - cos^2x) * 1 -
(sin^2x - cos^2x) =
=
sin^2x
-
cos^2x
-
sin^2x
+
cos^2x
=
= 0
Примечание
sin^2x и - sin^2x, а также cos^2x и - cos^2x взаимно уничтожились
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Answers & Comments
Verified answer
sin^4x - cos^4x - sin^2x + cos^2x == (sin^2x)^2 - (cos^2x)^2 - (sin^2x - cos^2x) =
= (sin^2x - cos^2x) * (sin^2x + cos^2x) - (sin^2x - cos^2x) =
Вспомним, sin^2x + cos^2x = 1 ==>
= (sin^2x - cos^2x) * 1 - (sin^2x - cos^2x) =
= sin^2x - cos^2x - sin^2x + cos^2x =
= 0
Примечание
sin^2x и - sin^2x, а также cos^2x и - cos^2x взаимно уничтожились