Hvordan forenkler du synden (x + (3π) / 2) cos x?

Svar:

# -Cos ^ 2x #

Forklaring:

#sin (pi + (pi / 2 + x)) cosx #

at vide det #sin (pi + alfa) = - sin (alfa) #

# = - sin (pi / 2 + x) cosx #

at vide det #sin (pi / 2 + alfa) = cos (alfa) #

# = - cosxcosx #

# = - cos ^ 2x #

Svar:

# -Cos ^ 2x #

Forklaring:

Udvide #sin (x + (3pi) / 2) "ved hjælp af" farve (blå) "additions formel" #

# farve (hvid) (a / a) farve (sort) (sin (A + B) = sinAcosB + cosAsinB) farve (hvid) (a / a) |))) #

#rArrsin (x + (3pi) / 2) = sinxcos ((3pi) / 2) + cosxsin ((3pi) / 2) #

#COLOR (orange) "Reminder" #

#color (rød) (bar (ul (| farve (hvid) (a / a) farve (sort) (cos ((3pi) / 2) = 0 "og" synd ((3pi) / 2) = - 1) farve (hvid) (a / a) |))) #

#rArrsinxcos ((3pi) / 2) + cosxsin ((3pi) / 2) #

# = 0-cosx = -COSX #

#rArrsin (x + (3pi) / 2) cosx = -COSX (cosx) = - cos ^ 2x #