Pitanje # 7218e

Odgovor:

Pogledaj ispod

Obrazloženje:

LHS = lijeva strana, RHS = desna strana

LHS =# (Sin (2 x + x)) / (1 + 2cos2x) #

# = (+ Sin2xcosx cos2xsinx) / (1 + 2cos2x) #

# = ((2sinxcosx) cosx + (1-2sin ^ 2x) sinx) / (1 + 2cos2x) #

# = (2sinxcos ^ 2x + sinx-2sin ^ 3 x) / (1 + 2 (1-2sin ^ 2 x)) *

# = (2sinx (1-sin ^ 2x) + sinx-2sin ^ 3 x) / (1 + 2-4sin ^ 2x) #

# = (2sinx-2sin ^ 3x + sinx-2sin ^ 3 x) / (3-4sin ^ 2x) #

# = (3sinx-4sin ^ 3 x) / (3-4sin ^ 2x) #

# = (Sinx (3-4sin ^ 2 x)) / (3-4sin ^ 2x) #

# = Sinx #

# = RHS #