4cosa.cos (60-a) .cos (60 + a) = cos3a?

4cosa.cos (60-a) .cos (60 + a) = cos3a?
Anonim

우리는

# rarr2cosAcosB = cos (A + B) + cos (A-B) #

# LHS = 4cosxcos (60 ^ @ - x) cos (60 ^ @ + x) #

# = 2cosx * 2cos (60 ^ @ + x) cos (60 ^ @ - x) #

# = 2cosx * cos (60 ^ @ + x + 60 ^ @ - x) + cos (60 ^ @ + x-60 ^ @ + x) #

# = 2cosx cos120 ^ @ + cos2x #

# = 2cosx cos2x-1 / 2 #

# = 취소 (2) cosx (2cos2x-1) / cancel (2) #

# = 2cos2x * cosx-cosx #

# = cos (2x + x) + cos (2x-x) -cosx #

# = cos3xcancel (+ cosx) 취소 (-cosx) = cos3x = RHS #