Решить уравнение tgx-4sin2x-2sin^2x=2cos^2x-ctgx

Tg(x) = sinx/cosx ctg(x) = cosx/sinx sin(2x) = 2sinx*cosx sin^2(x) + cos^2(x) = 1 (sinx/cosx) - 8sinx*cosx =  2(sin^2(x) + cos^2(x)) - (cosx/sinx) (sinx/cosx) - 8sinx*cosx + (cosx/sinx) - 2 = 0 (sin^2(x) + cos^2(x))/(sinx*cosx) - 8sinx*cosx - 2 = 0 (1 - 8(sinx*cosx)^2 - 2sinx*cosx)/(sinx*cosx) = 0 1 - 2*(2sinx*cosx)^2 - sin(2x) = 0 1 - 2sin^2(2x) - sin(2x) = 0 замена: sin(2x) = t, t∈[-1; 1] -2t^2 - t + 1 = 0 2t^2 + t - 1 = 0, d  =  1  + 4*2 = 9 t1 = (-1 + 3)/4 = 2/4 = 0.5 t2 = (-1 - 3)/4 = -4/4 = -1 1)  sin(2x) =  0.5 2x =  π/6 + 2πk, x=π/12 +  πk 2x = 5π/6 + 2πk, x=5π/12 +  πk 2) sin(2x) = -1 2x =  π/2 + 2πk, x=π/4 +  πk

                                                            решение: на интрвале (180; 270)  sina< 0  cosa< 0 tga=2tga/2/(1-tg^2a/2) tga/2=y 15y^2+16y-15=0 y=-5/3 y=3/5 sina/2/cosa/2=3/5 sina/2=x x^2=0,36-0,36x^2 x^2=0,36/1,36 sina/2=0,6/sqrt(1,36)=0,6/0,2sqrt(34)=3/sqrt(34) x^2=25/9*(1-x^2) 9x^2=25-25x^2 34x^2=25 sina/2=5/sqrt(34)

                                                                  реешение: сos3acos7acos5a=cos5a*(cos10a+cos4a)/2=1/2(cos5a*cos10a+cos5acos4a)= =1/2(1/2(cos15a+cos5a)+1/2(cos9a+cosa)=1/4(cosa+cos5a+cos9a+cos15a) 4cosa/2cosacos5a/2=4cosa(1/2(cos3a+cosa))=2cosa*cos3a+2cos^2a=cos2a+cos4a+2cos^2a= =cos2a+cos4a+1+cos2a=2cos2a+cos4a+1.