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sunnygirl312
@sunnygirl312
July 2022
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10 КЛАСС, ТРИГОНОМЕТРИЯ! Докажите 4
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mayli
Sin²x + sin⁴x + cos²x - cos⁴x = 1 - cos2x
sin²x + sin⁴x + cos²x - cos⁴x = (sin²x + cos²x) + (sin⁴x - cos⁴x) =
= 1 + (sin²x - cos²x)(sin²x + cos² x) = 1 + sin²x - cos²x = 1 + (-cos²x + sin²x) =
= 1 - (cos²x - sin²x) = 1 - cos2x.
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Answers & Comments
sin²x + sin⁴x + cos²x - cos⁴x = (sin²x + cos²x) + (sin⁴x - cos⁴x) =
= 1 + (sin²x - cos²x)(sin²x + cos² x) = 1 + sin²x - cos²x = 1 + (-cos²x + sin²x) =
= 1 - (cos²x - sin²x) = 1 - cos2x.