Решите тригонометрические уравнения, только полное решение ! 1) sin^2 x + 2sin x cos x- 3cos^2 x =0 2) sin^2 x - 4sin x cos x + 3cos^2 x =0 3) 2sin^2 x + 3 cos x =0 4) 8sin^2 2x + cos 2x +1 =0

                                        решение: 1) sin^2x+sin2x-3+3sin^2x=0 : cos^2x tg^2x-3+2tgx=0 tgx=1 x=п/4+пk tgx=-3 x=arctg(-3)+пk 2) : cos^2x  tg^2x-4tgx+3=0                                 tgx=1  x=п/4+пk                                 tgx=3  x=arctg3+пk 3)2-2cos^2x+3cosx=0     2cos^2x-3cosx-2=0     cosx=1/4(3+-sqrt(9+16))=(3+-5)/4 cosx=-1/2    x=п+-п/3+2пk 4)8-8cos^22x+cos2x+1=0 8cos^22x-cos2x-9=0 cos2x=-1 2x=п+2пk x=п/2+пk

x=-3, x=2

Объяснение:

Замена:

Обратная замена:

x\in \varnothing\\\\2)\;t=6,\; x^2+x=6\\x^2+x-6=0\\x^2-2x+3x-6=0\\x(x-2)+3(x-2)=0\\(x-2)(x+3)=0\\\left[\begin{array}{c}x=2\\x=-3\end{array}\right;" class="latex-formula" id="TexFormula4" src="https://tex.z-dn.net/?f=1%29%5C%3Bt%3D-4%2C%5C%3B%20x%5E2%2Bx%3D-4%5C%5Cx%5E2%2Bx%2B4%3D0%5C%5CD%3D1-16%3C0%5C%5C%3D%3Ex%5Cin%20%5Cvarnothing%5C%5C%5C%5C2%29%5C%3Bt%3D6%2C%5C%3B%20x%5E2%2Bx%3D6%5C%5Cx%5E2%2Bx-6%3D0%5C%5Cx%5E2-2x%2B3x-6%3D0%5C%5Cx%28x-2%29%2B3%28x-2%29%3D0%5C%5C%28x-2%29%28x%2B3%29%3D0%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%3D2%5C%5Cx%3D-3%5Cend%7Barray%7D%5Cright%3B" title="1)\;t=-4,\; x^2+x=-4\\x^2+x+4=0\\D=1-16<0\\=>x\in \varnothing\\\\2)\;t=6,\; x^2+x=6\\x^2+x-6=0\\x^2-2x+3x-6=0\\x(x-2)+3(x-2)=0\\(x-2)(x+3)=0\\\left[\begin{array}{c}x=2\\x=-3\end{array}\right;">

Уравнение решено!

1 бул + 4 бубл = 68

2 бул   + 3 бубл   = 76

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  булка - х

бублик - y

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x + 4y = 68

2x + 3y = 76

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x = 68 - 4y

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2*(68 - 4y) + 3y = 76

136 - 8y + 3y = 76

136 - 76 = 5y

60 y = 5y

y = 12

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x = 68 - 4*12 = 68 - 48 = 20

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ответ: 20 копеек и 12 копеек