Ax-5y-a=0, ПРИ (-1;5)
-a-25-a=0
-2a-25=0
-2a=25
a=25/-2
a=-12.5
<span><span>sin(arcsin 5/13+arcsin 12/13)=</span></span>
<span><span>=sin(arcsin5/13)cos(arcsin12/13)+sin(arcsin12/13)cos(arcsin5/13)=</span></span>
<span><span>=5/13*√(1-144/169) + 12/13*√(1-25/169)=5/13*5/13 +12/13*12/13=25/13+144/13=169/13=13</span></span>
Дано: sin α + cos α = 0,5
Вычислить: sin⁵α + cos⁵α
I. sin α + cos α = 1/2 возвести обе части в квадрат
sin²α + 2sinα cosα + cos²α = 1/4
1 + sin (2α) = 1/4
sin (2α) = -3/4
II.
sin⁵α + cos⁵α =
=(sinα + cosα)(sin⁴α - sin³α*cosα + sin²α*cos²α - sinα*cos³α + cos⁴α) =
=0,5((sin⁴α + 2sin²α*cos²α + cos⁴α) - sin²α*cos²α - (sin³α*cosα+sinα*cos³α))=
=0,5( (sin²α + cos²α)² - sin²α*cos²α - sinα*cosα (sin²α + cos²α) )=
=1= =1=
=0,5 (1 - (1/4)(2sinα*cosα)² - (1/2)*(2sinα*cosα) ) =
=0,5 (1 - (1/4) sin²(2α) - (1/2) sin(2α)) =
sin⁵α + cos⁵α =
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Использованы формулы
sin²α + cos²α = 1
2 sinα cosα = sin (2α)
a⁵ + b⁵ = (a + b)(a⁴ - a³b + a²b² - ab³ + b⁴)