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feho
@feho
July 2022
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Если sin x- cos x = 1/2, то sin^4 x+ cos^4 x =?
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Verified answer
Sin⁴x + cos⁴x = (sin²x)² + (cos²x)² =
= (sin²x)² + (cos²x)² +2sin²x*cos²x -2sin²x*cos²x =
= (sin²x + cos²x)² -2sin²x*cos²x = 1² - 2*(sinx*cosx)² = 1-2*9/64 =
= 1 - 9/32 = 23/32
Если sin x-cos x = 1/2, то
(sin x-cos x)²
= 1/4
sin
²x + cos²x - 2sinx*cosx = 1/4
1 - 2sinx*cosx = 1/4 (основное тригонометрическое тождество)
2sinx*cosx = 3/4
sinx*cosx = 3/8
(sinx*cosx)² = 9/64
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Answers & Comments
Verified answer
Sin⁴x + cos⁴x = (sin²x)² + (cos²x)² == (sin²x)² + (cos²x)² +2sin²x*cos²x -2sin²x*cos²x =
= (sin²x + cos²x)² -2sin²x*cos²x = 1² - 2*(sinx*cosx)² = 1-2*9/64 =
= 1 - 9/32 = 23/32
Если sin x-cos x = 1/2, то
(sin x-cos x)² = 1/4
sin²x + cos²x - 2sinx*cosx = 1/4
1 - 2sinx*cosx = 1/4 (основное тригонометрическое тождество)
2sinx*cosx = 3/4
sinx*cosx = 3/8
(sinx*cosx)² = 9/64