Знайдіть область значень функції у = х 2 − 4 х + 1 ;

2sin x - 4cos x - sin x/cos x - cos x/sin x + 2cos^2 x/sin x + 2 = 0

Умножаем все на sin x*cos x

2sin^2 x*cos x - 4cos^2 x*sin x - sin^2 x - cos^2 x + 2cos^3 x + 2sin x*cos x = 0

2sin x*cos x*(sin x - cos x) - 2sin x*cos^2 x + 2cos^3 x =

= sin^2 x + cos^2 x - 2sin x*cos x

2sin x*cos x*(sin x - cos x) + 2cos^2 x*(cos x - sin x) = (sin x - cos x)^2

(sin x - cos x)*(2sin x*cos x - 2cos^2 x) = (sin x - cos x)^2

2cos x* (sin x - cos x)* (sin x - cos x) = (sin x - cos x)^2

(sin x - cos x)^2*(2cos x - 1) = 0

1) sin x = cos x

tg x = 1; x1 = pi/4 + pi*k

2) cos x = 1/2

x2 = +-pi/3 +

Пошаговое объяснение:

    1) y = 12x+√x ;      y' = ( 12x+√x )' = ( 12x )' + ( √x )' = 12 + 1/(2√x ) ;

    2) y = 1/x + 4x ;     y' = ( 1/x + 4x )' = ( 1/x )' + ( 4x )' = - 1/x² + 4 ;

    3) y = 6√x+3x ;    y' = ( 6√x+3x )' = ( 6√x )' + ( 3x )' = 6/2√x+3 = 3/√x+3 ;

    4)  y = sin x + 3 ;    y'= ( sin x + 3 )' =  ( sin x )' + 3 ' = cosx + 0 = cosx ;  

    5) y = cos x + 2x ;  y' = ( cos x + 2x )' =  ( cos x )' + ( 2x )' = - sin x + 2 .