Hoe los je cos 2x + 3 sinx - 2 = 0 op?

Hoe los je cos 2x + 3 sinx - 2 = 0 op?
Anonim

Antwoord:

# S = {pi / 6 + 2pin, (5pi) / 6 + 2pin, x = pi / 2 + 2pin} #

Uitleg:

Gebruik eigenschap Double Argument:

# Cos2A = 1-2sin ^ 2A #

# 1-2sin ^ 2x + 3sinx-2 = 0 #

# 2sin ^ 2x-3sinx + 1 = 0 #

# (2sinx-1) (SiNx-1) = 0 #

# 2sinx-1 = 0 of sinx-1 = 0 #

# sinx = 1/2 of sinx = 1 #

# x = sin ^ -1 (1/2) of x = sin ^ -1 1 #

# x = pi / 6 + 2pin, (5pi) / 6 + 2pin of x = pi / 2 + 2pin #

# S = {pi / 6 + 2pin, (5pi) / 6 + 2pin, x = pi / 2 + 2pin} #