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Semionqwe
@Semionqwe
July 2022
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как это решать? sinx-cos x-4 cos^2x sin x=4 sin^3x у меня уже мозги кипят
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srzontmp
Sinx-cosx - 4cos^3sinx = 4sin^3x ->
sinx - cosx = 4sinx(cos^2x+sin^2x) = 4sinx ->
3sinx = - cosx -> sinx = - cosx/3
sinx^2 + cos^2x = 1 -> cos^2x + cos^2x/9 = 1 ->
10cos^2x = 9 -> cosx = - 3√10/10 cosx = 3√10/10
два равенства:
1. cosx = - 3√10/10 sinx = √10/10 ->
x = 3π/2+arcsin (√10/10) + 2πn
2. cosx = 3√10/10 sinx = - √10/10
x = 2π - arcsin (√10/10) + 2πn
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Answers & Comments
sinx - cosx = 4sinx(cos^2x+sin^2x) = 4sinx ->
3sinx = - cosx -> sinx = - cosx/3
sinx^2 + cos^2x = 1 -> cos^2x + cos^2x/9 = 1 ->
10cos^2x = 9 -> cosx = - 3√10/10 cosx = 3√10/10
два равенства:
1. cosx = - 3√10/10 sinx = √10/10 ->
x = 3π/2+arcsin (√10/10) + 2πn
2. cosx = 3√10/10 sinx = - √10/10
x = 2π - arcsin (√10/10) + 2πn